Any bb or cc cream that has 0 for ace in the ingredients list? or as close to 0 as possible

I love the Laneige waterbased cc cream because it's very light and blends into the skin well. I'd been using it for years now, and I never had any breakouts.

This may seem like a silly question, but what is the difference between a BB & CC cream? I've used BB creams, but not CC creams.