Both do essetially the same thing, they are both "wireless broadband technologies." The difference lies (partly) in their reach and who's utilizing the technology.
Wi-Fi is intended for small hotspots with very short range (200 yards), and is used by individuals.
WiMAX is designed for long-distance (up to 10 miles), and is mainly used for wireless Internet service providers.
I found this cool diagram that displays how WiMax works.
Lyte