People do use these terms interchangeably, but there is a difference. Correctly, a casserole is a large dish with a fitted lid, used for slow cooking; the word also applies to anything cooked in such a vessel, even if the cooking process is relatively fast, as with pre-cooked meat, for example. Traditionally a casserole dish is cooked in the oven. Stewing is a slow method of cooking, especially suitable for tenderising tough meat, and traditionally is done on the hob or over an open fire. Nowadays we don't make much distinction between the two, though there is a tendency to use the word "casserole" more than "stew."
Whatever you call them, slow-cooked dishes are a great idea if you are busy. At their simplest, they just involve throwing in whatever meat, vegetables and seasoning you have, covering with liquid, bringing to the boil and leaving (in the oven is probably safer if you're going out) for a couple of hours.

A cassarole is usually baked with meat and veggies .a stew is made on top of the stove.