Qualcomm sabotaged 4G

WiMax = wireless microwave something something = "4G"
LTE = "4G LTE"

they're different technologies. Speeds are fairly similar, though the standards documents suggest that WiMax is faster if you're moving around and LTE is better if you're stationary (i.e. LTE for browsing on your phone at starbucks, and WiMax if you're on a bus or train) but at the end of the day they both put out similar speeds.

Anyway, Qualcomm basically bribed Apple not to make a WiMax phone, and as a result iPhones only ever supported LTE which meant you couldn't get them on Sprint. It ended up killing both Sprint and WiMax.

WiMax also doesn't use a SIM Card, so you can thank Qualcomm if you've ever been inconvenienced because of a SIM.