A stew generally involves the braising of some meat in bite sized chunks in liquid at fairly low heat, thus slow cooking, and includes vegetables that may be added at different times during the braising time. Braising can be done on the stove top or in the oven.
A casserole is virtually always baked in the oven, and will involve multiple ingredients that may or may not include meat of some kind.
Both of these tend to be considered as meals in one dish, though many people will add accompanying dishes such as fresh salads.
This description is from my own experience. If you google the definitions of stew and casserole you may find they vary from mine.