This has been asked several times before. The most commonly held view seems to be that the ingredients are the same but the cooking methods are different. (i.e. a casserole goes in the oven, whereas a stew is cooked in a saucepan on the hob).
Correct...stew in saucepan on top of cooker...can be cooked slowly at a lower cost than cooking slowly in an oven. I prefer lower cost, tastes the same and cheaper, my style of cooking. No difference in taste, I'm a cheap gal at heart, preferring to spend my dosh on a nice aperitif and some tasty appealing um...or gin...or lol. lol.
A lot of terminology is dependant on how and where you are eating it - in an upmarket restaurant you may order 'Gently braised pigs cheeks with a piquant sauce..
At home - 'Nip to the butchers for some odds and ends and ask him to put it on t'slate till Friday, I'll cobble some thing together'.