Potatoes au gratin consists of thin slices of precooked potatoes, baked in cream with layers of potato and cheese, and a cheese topping - making it a rather decadent and rich potato side dish. Potato dauphinoise also consists of thinly sliced potatoes cooked in cream (although the potatoes haven’t been pre-cooked) but this dish usually doesn’t include any cheese when made traditionally.  Scalloped potatoes are similar to potato dauphinoise except that the potato rounds are usually thicker than what you’d use in potatoes au gratin or dauphinoise.