Is there a difference between an undergraduate and an honours thesis? I came across the latter during some online research on US colleges and it seems to me that honours are only known in those institutions. Is this correct?

Moreover, it seems that some colleges offer normal undergraduate as well as undergraduate honours studies/classes/degrees. I heard that the difference is that the latter have to write a thesis while the former seemingly don't. Is this correct and are there other differences?

Does this separation also exist on the Master's level and graduate schools?