A dermatologist but these terms are more descriptive terms for marketing purposes than for dermatologists. If your skin gets oily then it's oily unless you have dry patches as well or normal area. Then you'd be combo. Ance prone is basic, if you tend towards breakouts you are acne prone. The main point is to help you pick products in the right texture and to describe your skin to others.
Oiliness can be a sign of dehydration. The skin over produces oil if it's dehydrated. Some skin is just oily.