You may be confused by what you can see in stores, most stores sell "Sparkling Cider'' or ''Sparking Juice'' this is misleading, because basically all of these are non-alcoholic drinks. Unlike in the UK and plenty of other places around the world, cider does not mean alcoholic in america.
But yeah to answer your original question, you have it right. For sweetness you can have very dry, dry, semi-sweet and sweet generally. But you can also have still (non-carbonated) or sparkling (carbonated). Or any combination of those two characteristics.