Hi Molly and welcome to the board.
Well, sometimes it's a matter of personal preference. I have a tomato soup recipe that calls for heavy whipping cream but I use half and half because with the heavy whipping cream it is soooooo rich I feel guilty eating it! :roll: And, it's much thicker. Whipping/heavy cream does not ALWAYS interchange with half and half though.
If it's used in a sauce that is supposed to be thick and the recipe called for heavy whipping cream you would probably want to use it. I wouldn't assume, without looking at a recipe, that I could use half and half in its place.
Whipping cream or heavy whipping cream does whip, half and half does not whip. So if it's whipped cream you want then "whipping" cream is what you need.
Was I close to answering your question? There are more knowlegeable people here on the board that could answer this question I'm sure. Hopefully they'll chime in.
Hope to see you around the boards!