I am trying to figure out the difference between a press from a clean and press and an overhead press?
They are the same (strict press) if you're talking about the competition "clean and press". If not then it's up to you.
Is it cheating to do an overhead press with a small squat for momentum?
Yes it's "cheating" and it got its own name, "push press".
I think adding a session of push press can be beneficial if you want to increase your press number because you still gain the benefit of handling heavier weight in the negative phase. It might not be transferable at all but might be worth trying (I'm doing it).