Dana Blankenhorn explains the differences:
Wi-Max is designed to send big hunks of data over vast distances. It’s a wholesale technology. Wi-Fi is designed to send somewhat-smaller chunks over much smaller distances. It’s a retail technology.
Wi-Fi continues to move ahead. The next version, 802.11n, will run data at over 100 Mbps. There is going to be a crying need for backhaul, not just long-range backhaul but medium-range as well.
If you can’t get your collection of Wi-Fi traffic out to a competitive fiber node you’re going to be at the mercy of the Bells, who sell T-1s through an eye-dropper, with an aim toward putting you out of business and taking it all over for themselves to subsidize their wires.
That’s where Wi-Max comes in. Wi-Max can do that job, and do it quite easily.