Swords
Swords are long edged weapons, generally designed for thrusting and slashing. Growing historically out of knives and daggers, swords evolved to become implements of war and sport. Thrusting swords, those designed for swordplay and fencing, became wildly different in design and balance from those swords meant for slashing. Although both could, technically, be used for similar motions, each was designed more for the context of use. You generally wouldn't take a fencing sword onto the field o muddy, bloody combat (at least, not if you were expecting to get through a shield wall any time soon).
Within the bounds of the Castlevania series, the two types of one-handed swords evolved different motions within the game series. The thrusting swords, like epees and rapiers, have a similar use (and speed) as knives and daggers. Meanwhile slashing blades became the "standard" sword used in all of the Metroidvania games.
About Swords:
History of Swords
Although most would think of swords being introduced into the Castlevania series with Alucard and his adventure in Castlevania: Symphony of the Night, the actual first instance of a sword hails all the way back in Haunted Castle, the "off-brand" Castlevania arcade title. There hero Simon Belmont gains the sword as his final upgrade for his whip, marking the first and last time Simon ever used a sword as his primary weapon.
After that we then do transition over the Alucard as Symphony of the Night introduced whole new classes of weapons, including an entire fleet of swords to choose from. Alucard could use knives and short swords as well as longer swords (and two-handed great swords), although the short swords and one-handed blades all used a similar, faster sweeping motion. Alucard's preferred sword (the one that is referenced regularly, is the Alucard Sword, a powerful sword (and family heirloom) that enabled Alucard to perform a magical teleporting slash. Although other swords in the game could arguably perform more damage over time, the Alucard sword had the single more power slash of any weapon in the game. It is also the sword he used again later in Castlevania: Dawn of Sorrow (and presumably also in Castlevania: Legends).
After Symphony of the Night swords only made their return again when non-Belmont characters were in the lead, starting with Castlevania: Aria of Sorrow. These games included Castlevania: Dawn of Sorrow, Castlevania: Curse of Darkness, Castlevania: Portrait of Ruin, and Castlevania: Harmony of Despair.
Finally, in Castlevania: Lords of Shadow 2, two more swords are used. The Void Sword, a sword with the power of holy ice, grant hero Dracula (aka Gabriel Belmont) the power to freeze, as well as the ability to leech energy out of his enemies via his attacks. Alucard, meanwhile, gains the Crissaegrim (known in other games as the Valmanway) as his powerful sword (in place of the Alucard sword). This is the sword he uses to lock Dracula away for 500 years until the events of the second Lords of Shadow game, and then uses for his attacks late in that title.
Swords in Combat
In Castlevania a sword is identified not only by its icon but also by the way it is swung. A proper sword (in the context of the series) has a forward slash, often denoted by a tight, frontward loop. Swords tend to be slower then daggers and knives but deal more damage while still being faster (by weaker) than great swords. This makes them idea for quick combat, especially when combined with the "jump cancel". In most Metroidvania entries in the series, a hero will be able to jump and slash, having their attack cancel out when they hit the ground allowing them to move again, or take a second attack quickly. This can be a great way to maneuver through combat or to layer on damage against foes. Note that not all weapons allow for jump canceling but most swords will allow it.
Notably, many magical swords in the series have special attacks that can be performed with button combos (such as down, down-fowrard, and then forward plus attack). The Alucard Sword is a famous example as that attack allows Alucard to teleport forward temporarily and slash at an enemy from behind. Although special moves aren't included in every game, they became a standard of magical weapons in the DS entries.
Historic Swords
It is worth pointing out that the English names and terms for swords are pretty fluid and don't always align to specific blades or blade types. A "short sword" is simply a term that applies to a blade of shorter length (similar in style to a "long dagger" or "dirk") while a "long sword" commonly refers to a longer blade, generally a two-handed weapon. But those terms aren't always applied evenly and can mean different things in different eras.
Bakatwa
This is a straight, short sword hailing from Southern Africa. It was mistranslated as "bekatowa" in Symphony of the Night.
Bastard Sword
A class of "long swords", generally meant to be used two-handed. The term "bastard sword" comes from the fact that these sword could be swung "hand-and-a-half", with the name coming into common use in the 19th century as the term "long sword" was associated at the time with longer rapiers.
Broadsword
A wide-bladed sword with a basket hilt, commonly associated with military use. The term "broadsword" came into use in the 17th and 18th centuries to describe double-bladed swords with the distinct basket hilt, although the term is more loosely applied now to all weapons matching this description (no matter the era). The schiavona is a type of Italian broadsword.
Cutlass
A broad, short sabre favored by the English and French Navies during the height of their naval empires. The weapon's name likely derives from the French name coutelas.
Damascus Sword
Strictly speaking not one type of sword but really the name for the steel that made up the sword. Damascus steel was made from Wootz steel ingots and produced very strong steel with a distinctive pattern of bands and mottling. These swords are prized for their strength and cutting power (although some of that perceived power may be more story than fact).
Falchion
A European sword with a single edge meant to be used one-handed. Although depicted in the Castlevania series as a curved sword, the weapon was more machete-like in design and construction. It could have a broad (even weighted head) making it comparable to the Turkish kilij (a scimitar-class weapon) in cutting power.
Gladius
The standard sword of the Roman infantry, this weapon was inspired by the Celtiberians in Hispania, giving it the proper name of gladius hispaniensis ("Hispanic Sword"). The gladius was standard issue for a Roman solider along with their shield, javelin, and dagger.
Jagdplaute
A hunting sword (or hunting saber) is a sword attributed to France designed for the purpose of hunting deer. It was a shorter sword with a slightly curved blade.
Saber
The saber (or sabre) is a backsword (a single-bladed sword with a flat back, meant to be used one-handed) that was favored in cavalry by much of Europe, up through the Napoleonic era.
Scimitar
Technically the scimitar is a class of weapons, single-edged swords with curved blades associated with Middle Eastern and Northern African cultures. The term "scimitar" is of European invention and the category includes the Indiana talwar and the French badelaire (both of which are swords in the series).
Swords of Legend
Agni's Flame
First called the "Firebrand" in Symphony of the Night, Agni's Flame is a sword made from the fire of the Hindu god Agni. It's worth noting that the fire god makes his own appearance in the series in Castlevania: Dawn of Sorrow as the demon Aguni.
Alucart Sword
A joke sword in Symphony of the Night, this weapon is a cheap knock-off of the real deal Alucard Sword, meant to catch players off guard until they realize the truth.
Caladbolg
Written as "Kaladbolg" in the series (and sometimes referred to as Caladcholg in mythology), this dark blade was wielded by Fergus mac Roich from the Irish "Ulster Cycle". It was said to be powerful enough to take out groups of men at once, as well as cutting the tops off of hills.
Crissaegrim
Technically this name refers to two swords in the series. The first, introduced in Symphony of the Night, was a multi-hit sword that would later be called the Valmanway in further titles. Meanwhile the name "Crissaegrim" would be applied to Alucard's sword in Lords of Shadow 2. It was forged by Alucard from the tip of the Vampire Killer and the remains of two other swords, creating a powerful blade.
Dainslef
Is is, confusingly, three different swords that have all been mixed together over the course of the Castlevania series. In the series the Dainslef was first called Gurthang, a sword that got stronger when bloodied, but then the name was changed to Dainslef in later appearances. This likely because another sword in Symphony of the Night was called Mormegil, which as another name for the Gurthang. In Tolkien's stories the Anglachel was created by the Dark Elves and then later reforged into Gurthang ("Iron of Death") by Turin although the orcs and elves called it Mormegil ("Black Sword"). Meanwhile, Dainslef comes from Norse Mythology. It was the sword of King Hogni, forged by dwarves to create wounds that would never heal.
Fragarach
A sword hailing from Celtic mythology. It was wielded by Manannan mac Lir before passing through ages to Conn of the Hundred Battles. It was forged by the gods with the power to defeat all armor.
Glamdring
Called the "Dark Blade" in Symphony of the Night, this one of a number of swords from Tolkien lore to show up in the series. An elvish blade (like Sting and Orcrist), this sword would glow in the presence of Orcs. it was picked up by Gandalf and used throughout the Lord of the Rings saga.
Gram
Sword of the famous Norse hero Sigurd. Passed to him by his father Sigmund, Sigurd later used the blade to kill Fafnir, a dwarf who turned into a dragon (because Norse mythology is all pretty dark and silly at the same time).
Harpe
Called Harper in Symphony of the Night, this blade was used by Perseus. Given to the hero by his father, Zeus, the sword was later famously used to behead Medusa.
Hrunting
This is the famed sword of Beowulf, the hero of his own epic Germanic poem. Hrunting was a supposedly powerful sword, but it proved useless in Beowulf's battle against Grendel's Mother. In the Castlevania series Hrunting is a poison sword, usually powerful through the mid-game of many titles. Of note, the sword was first called "Terminus Est" in Symphony of the Night before being renamed to Hrunting.
Joyeuse
A very pretty sword said to be made out of gold (which, frankly, would make for a very weak sword considering how soft pure gold really is). The name comes from the personal sword of Emperor Charlemagne. Of note, he sword has the swing of a great sword in Aria of Sorrow, but then a more standard sword swing in Dawn of Sorrow. it's also worth mentioning that in Castlevania: Grimoire of Souls, the sword is described as having "The Spear of Longinus" within its pommel. Presumably that means the spear head was used to make the pommel as otherwise that's a very long and unwieldy pommel.
Katzbalger
This was an Medieval arming sword (a short blade used by pikemen and archers) preferred by Germanic mercenaries of the 16th and 17th centuries. Sometimes conflated with a broadsword, although the construction was different in the pommel and hilt.
Laevatain
A more powerful fire sword within the game series, acting as a kind of upgrade over Agni's Flame. The sword comes from Norse mythology and was forged by the elves. It proved too powerful, though, with the ability to damage even the gods themselves, so it was taken to Asgard (where it was later used in Ragnarok, the end of the world). Meanwhile, in the American translation of Symphony of the Night the sword was called "Marsil", which is thought to be a mistranslation of Narsil, the sword from Tolkien's lore that cut off the hand of Sauron.
Mourneblade
The Mourneblade is a sword that steals life from enemies as it attacks them. It comes from the works of Michael Moorcock and is described as a sentient demonic sword.
Mystletain
In Norse mythology it was foretold that a weapon would be made that would kill Baldur (which would then usher in Ragnarok, the end of the world). Frigg, Baldur's mother, made every object in the world swear it would not harm Baldur, and all but one agreed. That one, the mistletoe, was later used by Loki, the Trickster, to create a spear that indeed as then used to kill Baldur. his is thought to be the Mystletain, although it appears as a sword and not a spear (or sometimes an arrow) as it was in the myths.
Orcrist
Called the Luminus in Symphony of the Night, this blade hails from the works of Tolkien. It's an Elvish-forged blade that, like other blades of its type (such as the famous Sting), would glow in the presences of orcs.
Rahab's Frost
First called the "Icebrand" in Symphony of the Night, Rahab's Frost is a strong ice sword. It is likely a reference to Rahab, the sea dragon of Jewish mythology, a creature of the dark abyss. It's worth noting that while the sword was first called the "Icebrand" (in the American translation), a later sword would also be called "Icebrand" but that was a different (and more powerful) weapon.
Stellar Sword
The five-bladed sword used by Maxim Kischine (and later Johnathan Morris) in the series. The five blades can be used together to create a single, fast sword slash. They can also be fanned out and thrown like a shuriken, which then travels out and back (in a pattern reminiscent of boomerangs). The "stellar" part of the name comes, presumably, from the star-like shape the blade can take on, as well as it's holy (i.e., celestial) element.
Sword of Hador
The sword of the House of Hador, a great family in the stories of Tolkien. It was crafted in the First Age and given to Hador, becoming an heirloom of the family.
Tirfing
Called Tyrfing in the series, this sword hails from Norse mythology. It is a cursed dark sword that, appropriately in the games, subtracts ATK rendering the sword pretty useless. In the myths the sword was made by dwarves against their will so they cursed it to kill any man their used it (among other evils the sword would go on to cause).
Valmanway
Called "Blessed Wind", the Valmanway (first called the Crissaegrim in Symphony of the Night) is a sword that slashes multiple times when the attack button is pressed, but the sword has no wielding animation. The hero using the sword can move freely while the blade attacks, and in fact the attack button can be pressed repeatedly to layer on attacking damage. It is thought that the name for Valmanway comes from Tolkien. (like so many swords in this series), with the sword's name literally translating as "power of the blessed one", referring the Manwe, the god of air and wind.
Vjaya
Forged from one of Indra's thunderbolts, the Vjaya (also called Indra's Light in the series) hails from Hindu legend. It's a powerful lightning sword that can hit multiple times per swing. First called the "Thunderbrand" in Symphony of the Night (as so many swords were given weird names in that game).
Vorpal Blade
First appearing in Symphony of the Night, the Vorpal Blade has absolutely no wielding animation; when the player touches a button the sword slash comes out but Alucard can keep moving normally. This allows the player to repeatedly tap the attack, swinging wildly and quickly while maneuvering in the process, making it quite powerful. For sheer number of attacks the sword is only outclassed by the Valmanway. The name "Vorpal Sword" comes from "Jabberwocky" by Lewis Carrol, a nonsense poem from 1871. It has then gone on to be used in a number of RPGs, generally to indicate a very powerful, and very sharp, sword.
Other Swords
This page covers the standard swords found in the series, those with a natural forward slashing motion. However, there is another class of swords, Great Swords, which have a slower over-head slashing motion. These swords, along with battle axes, count as their own category of weapons within the bounds of the Castlevania series.
One other class of swords are the katanas. This group of weapons originally started as a subset of standard swords (one- and two-handed in Symphony of the Night) before growing into their own class of weapons with a wider, circular motion to their attacks.