Perspective means "point of view, especially the ability to see the whole of something." In art, it specifically means the ability to present three dimensional objects using a two dimensional medium. Perspective is normally a noun.
The prefix per- means "completely."
Prospective means "future or potential" and is normally an adjective. The noun form is prospect.
The prefix pro- means "forward."
The Latin root of both words, -spect-, means "to see." So perspective literally means "seeing completely" and prospective means "seeing ahead."