What is WiMax?

WiMax is the successor to WiMax, and follows the IEEE 802.16 standard as opposed to 802.11 we know and love. It allows much longer distances, up to 30 miles or so, vs WiFi's 300ft.

It uses completely different electronics, and different frequencies, but equipment can be produced that does both.

This technology is being used by cell phone companies like Sprint to supply high speed wireless internet to their customers as infrastructure as opposed to WiMax which is so short range it tends to be privately owned directly by the customers ( like homes or businesses ).

A good description can be found here:
PC Today Article - WiMax & Pre-WiMAX