well I think the biggest diffrence is in the history, mauy thai is a thai form of boxing, kickboxing came out of full contact karate in the US, the rules are diffrent but their both ring sports. There are alot of variations on "kickboxing" rules that range from almost being western boxing to almost being mauy thai.
some kick boxing you can't kick below the waste, this is the same kick boxing that has a minimum number of kicks you can throw (because no one would throw kicks otherwise), than there is some where you can kick anywhere, and there is some where you can use your knees.
Mauy thai in the US is very simular because in most states you can't compete using elbows, the only big diffrence being the clinching rules and the use of the shin in a kick. internationaly the rules differ more though and the use of elbows changes things alot.