I THINK I know what belling is - that curved flare at the very top of the case mouth, larger than the bullet diameter, but just the top few mm, to prevent shaving the bullet and so it sits atop the case properly on indexing....(right?).
What's your definition of expansion, then, compared to belling?
Yes you are correct, the belling/flare is the case mouth expansion die/step that allows bullet seating without shaving the diameter down. The terms are treated interchangeably when discussing pistol reloading.
Maybe understanding the "why" would explain more.
? All brass varies in wall thickness. No 2 brands use the same dimensions. That's fairly well known and understood.
Question: So how can the die maker re-size the exterior of the case, so that you get perfect
case neck tension ? That's is to say, how can one squeeze on the
outside of the case to get the
inside of the case to be a
perfect size... given that all brass varies in wall thickness ?
Answer: You can't !!
Solution: The dies squeeze (re-size) the outside of the case
smaller than what you need, then go back and open the inside with a
second operation. That secondary operation is called "expansion", and is done by pushing a perfectly sized plug into the case mouth interior to open it up to the desired inside dimensions.
Try sending one piece of brass though your die set and make measurements after each die, you'll see what I'm talking about. In some instances, the dimensional changes can't be seen with the naked eye. Remember that the dies are also accounting for "brass spring-back" along with varying wall thicknesses. The ability to do this accurately on thousands of die sets is really a miracle of modern manufacturing. Truly mind-boggling in scope.

Hope this helps.
