Just a quick set of broad categories:
Longswords - generally speaking, a medieval/renaissance period sword of two edges, with a blade of 3+ feet and a grip large enough that it was intended for two handed use but could be used for specific one handed techniques. encompasses the broad category of weapons such as the type XIIa and XIIIa 'great swords of war' and later more defined weapons such as the 'true' longswords.
Great Sword:
http://www.albion-swords.com/swords/alb ... -xiiia.htm
Long Swords:
http://www.albion-swords.com/swords/alb ... ck-xva.htm
http://www.albion-swords.com/swords/alb ... xviiib.htm
Backswords - another broad weapon type. Basically defined as a single-edged blade, predominantly slashing though with certain thrusting characteristics. So called because the 'back' of the weapon was a thick, rigid portion tapering down to the frontal edge.
This category includes weapons of either straight blades such as certain basket-hilted claymores/schiavona and curving weapons such as the cutlass, saber, or katana. Indeed, most curving blades with the edge on the outside of the curve can loosely be termed 'sabers' as well.
Rapiers/Side swords - broad (seeing a pattern here?) category of weapons again. Essentially a development of largely civilian swords that evolved out of the 'arming' or knightly sword. Single-handed, often with a complex hilt ranging from a simple nagel side ring to protect the hand to a full on spanish cup hilt.
In essence, the distinction is between 'true' rapiers that were very slender weapons with less of a cutting edge, designed for the long distance lunge into someone's guts, and side swords which tend to have a broader blade and be suited to the cut a la George Silver's preferences. Note that the distinction is largely a modern one, back then most people simply called it "a sword."
Rapier:
http://www.albion-swords.com/images/swo ... apier2.jpg
Side Sword/Cut and Thrust sword:
http://www.albion-swords.com/images/swo ... ro/c&t.jpg
as for the 'style' of the combat used with these, see George Silver for the sidesword, also Fabris. For rapier, I cant recommend anything higher than Cappo Ferro, but be warned as the examples show very naked men.
From there you have the 'true' two handed swords (getting confused yet?), such as the portugese montante, the italian spadone due mane (sword in two hands), and the german zweihander. These have fewer treatises that I'm aware of compared to the -massive- corpus of works on longsword. However, there are a few manuals that illustrate such weapons. Their broad technique was for the control of large bodies of men, such as the employment of the Zweihander troops (called doppelsoldner) against pikemen for the purpose of line-breaking.
Hope this clears up a few things about the broad weapon types.
