In addition to what Michael Chambers just said, you can also use "wait on" in a different way. You can say "I will wait on the train", which could mean that you are waiting while on the train. This could mean "waiting while on the train" or it could also mean "I wait on the train to arrive". Because this has two meanings, it's often safer to just you "wait for".

In ordinary speech, they mean the same, but "wait for" is more common. "wait on" is the specific verb to describe the activity of waiters. They "wait on" tables.