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wimax or 802.16 is used for metropoliar area access network which means u can service a larger area than a hotspot. and can be used ptp and p2mp .
in p2p wimax can connect nodes in 72 Mbs and a distance of 50Km,but in p2mp the wimax mast can service an area about 13 Km of radius,but wifi or 802.11 has smaller cell ( radio range ) and it needs mesh networking like cellular mobile phone to cover a large are.the maximum speed is 54 Mbs in p2p connection,and it dramatically decreases if users grow in an cellular area.
Wireless Fidelity (Wi-Fi)
The popular term for a high-frequency wireless local area network. The consumer-friendly name for the 802.11b engineering standard. It lets home and office users create wireless local networks, which connect two or more computers to each other and a faster Internet line. This way there is no more poking holes in walls or tripping over bulky Ethernet cables. The Wi-Fi technology is rapidly gaining acceptance as an alternative to a wired local area network (LAN).
WIMAX(World Interoperability for Microwave Access)
An organization founded in 2001 that promotes the IEEE 802.16 wireless broadband standard and provides certification for devices for compliant devices. WiMAX is designed to extend local Wi-Fi networks across greater distances such as a campus, as well as to provide last mile connectivity to an ISP or other carrier many miles away. In addition, Mobile WiMAX offers a voice and higher-speed data alternative to the cellular networks
In short they are two different standards for different function by IEEE.
WiMAX is more like commercial application while WIFI is more like small LAN users which is supposed to be office area network or something like that.