I think I have got a pretty good grasp of the different "whats" in Korean, but correct me if I am wrong!
무엇 = What ('what is this')
무슨 = What type/kind - (Adidas vs Nike, Croissant vs Baguette, etc)
어떤 = What quality of (big, small, soft, hard, square, round, etc.)
어느 = Which ('This one or this one?' 'What (Which) one do you like?') Hope this helps!