How is being in a coma different from being under anesthetia?

Same thing: General anesthesia is medically induced coma, controllable by the anesthetist, hence predictable and reversible. Non anesthetic coma is a huge topic with innumerable causes and hence results. Duration of cdoma can be from microseconds to forever.

See below: In some ways an anesthetic is a chemically controlled coma. However, in a coma we cannot reliable predict if and when the patient will wake.