Most weapons are going to be minor variations on a theme, for instance if someone showed me a shamshir and a scimatar I probably wouldn't be able to tell them apart.
Sword categories I can think of off the top of my head are straight (long sword, rapier, falchion), curved (scimatar, katana, cutlass), straight
and curved (khopesh) one edged (all curved that I know of, and some straight) double edged (straight) long and short. Then there are claymores and zhweihander (sp?) which are practically polearms...
Do you just want us to start listing off weaponry?
This post is kind of rambling already so I'll add this here. The link you have to a falchion is not a falchion.
This is a falchion. They are essentially long cleavers.