Welcome to the forums Matt
I'm no expert but as a chippy I've done a lot of plastering jobs, and as far as I'm concerned they're interchangeable. I've used cornice as base, and base as cornice.
I think cornice cement goes off a bit quicker, and has a better initial grab, so you can push a cornice into place and it will stay there after holding it in place for a few less seconds, but I've used base before and I haven't had any call backs.
For a small job, rather than buying two products, I'd just get a 20kg of cornice and use it for everything. You can put a bit of citric acid (lemon juice or orange juice) in it to slow it down, or as our resident expert Rod has told me, you can use salt to speed it up.
He'll probably be along shortly, and he'd have all the right information on this one I'd say. I'm interested myself.