When you "come across" something, you discover it for the first time. When something "comes about", it is created at that very moment. You wouldn't "come about" someone else's idea, but you could come across it.

In general, "come across" means to find or discover, usually in a haphazard way and in a situation where you were not originally looking for the thing that was discovered. Another phrase that means the same thing is "to happen across" or "to happen on." To "come about" means "to originate."