WiMax is used for WAN access by some ISPs. It's not used for cellular services, only for cellular backhaul.
WiMax is somewhat similar to Wi-Fi but has carrier features and much longer reach. It's completely different from traditional cellular services, the differences would most likely fill a book.
For a start, you can find overviews here
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and primers and standards here
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What technology an ISP uses is entirely up to them. Technologies like WiMax and WLL are in some use, Wi-Fi is also used for short range and hotspot coverage.