In the first FF games, Haste actually worked as a kind of Hit-increaser, that allowed your chars to hit the enemies more often with each attack chance.
This was eventually changed, though, and since then it has mostly worked as a plain Speed-increaser that makes your characters act faster.

Which one do you prefer?
Personally I always liked the Hit-increaser version better, because I love how the characters start dealing 10 hits per attack all of a sudden.