3G, 4G are referred to as generations... no real "standards" as it was initially a coined term from a Japanese company that got adopted as a marketing term.
but it categorizes relative speeds/technology when it comes to wireless connections, like 3G with EDGE, EVDO Rev 0/A. And even then categories are determined by the carriers and not some standard, even though there is a push for some sort of standardization I doubt the carriers want that so they can call things whatever they want.
WiMax and LTE are actual technologies in the 4G area, HSPA+ for GSM service can be considered 4G but depends on who you ask, I think they just released 42MB/s HSPA+?
WiMax and LTE are basically similar speeds, don't know why people think one is "faster" than the other, it all depends on how much bandwidth the service provider gives you. Not too many Verizon phones with LTE capabilities, several states still w/o on both LTE and Sprint. So if you were one of the few using LTE in your neighborhood you got amazing speeds, but not like Verizon is trying to give each user some ridiculous dedicated speed. I think under current specs both WiMax and LTE have about the same max speed capabilities in theory, with WiMax having slightly more under current specs.