Anesthetist –  someone who administers anesthetics, usually a specially trained advanced practice registered nurse with graduate-level education in anesthesiology..

Anesthesiologist –  a physician trained in anesthesia and perioperative medicine. In the United States, the term anesthesiologist refers to a physician who has completed an accredited residency program in anesthesiology, usually four years following medical school either with an M.D. or D.O. degree.