To (be able to) afford something means you have enough money/time/etc for it. It usually comes with some form of "can" or "be able to". Without a form of "can", it means "to provide", but this is a fairly rare usage.
To offer something means you present something in the hope that the other person will take it.
I can only find one example where they would have a similar meaning. Almost all of the time the meanings are clearly different.