Wifi was and still will be used in LAN environments for the foreseeable future. WiMax, on the other hand was designed to provide (MAN) Metropolitan Area Access, to homes and businesses.
WiMax base stations will have the ability to provide approximately 60 businesses with T1 access and hundreds of homes with DSL/Cable speed access…in theory. Engineers are stating that WiMax has the capability of reaching 30 Miles but real world testing has shown 4-8 mile working radius.
WiMax (MAN) deployments are similar to a WiFi network. First the ISP would have their T3 or higher access. The ISP would then use line of sight antennas (Bridges) to connect to towers that would distribute the non line of sight signal to (MAN) residential/business clients.
WiMax line of sight antennas operate at a higher Frequency up to 60mhz. The distribution antennas do not have to be in the line of sight with their clients.