Japanese swords evolved from Tang Dynasty swords from China.
Tachi: usually wielded from horseback, they tend to have gaudier fittings similar to Tang Swords, most importantly the koshiate hangers from which they are mounted.
Handachi: a Katana with tachi fittings, save for the koshiate hangers.
Katana (Uchi-gatana): the iconic Japanese curved sword.
Wakizashi: paired with a Katana, the blade is shorter.
Tanto: a short stabbing dagger.
O-Katana: a large katana, with a blade length of 30-33 inches.
Nodachi/Odachi: a large sword, with a blade of over 84cm/34 inches.
Iaito/Mogito: a blunt training sword
Japanese swords also have varying geometries:
Shinogi Zukuri: the standard, iconic shape, with a defined yokote (horizontal plane) at the kissaki (tip).
Shobu Zukuri: shape is similar to a Shinogi Zukuri, except that it does not have a yokote
Unokubi: literally, cormorant's neck. The blade thins near the kissaki, making it a light and nimble sword. The geometry is based on the naginata.
Kogarasu: A transitional geometry, as Japanese swords evolved from the double-edged, pointed Tang straight swords.