Here's a brief explanation of various words for different types
Different swords may have different names due to their different class, style, or function, but mostly, different words came about more due to cultural aspects, i.e. the sword's origin, region, and history.
saber: curved, thin, single-edged blade of European origin.
rapier: straight, very thin, trusting weapon, usually with fancy guards. European origin.
cutlass: Saber-like, but very curved, thick, shortish, slashing knife. (think of pirate's swords in movies).
scimitar: Saber-like, but very curved, thick, heavy cutter used in Middle East.
(Think of the tales in
katana: Saber-like, two-handed. Japanese Samurai (warrior)'s swords.