Precisely so. An anesthesiologist is a physician with special training in the administration of anesthesia,and all that that entails. He or she may well work in a department with less-trained people who do similar things, but without as much responsibility, remuneration of course, and also [supposedly] knowledge of other disease states that may have an impact on the case (i.e. pre-operative assessment), or the ability to recogize things that are going wrong as quickly. In the US many hospitals employ Nurse Anesthetists, sometimes more than physician anesthesiologists.

There is an analogous distinction between optometrists and ophthalmologists: same field, do much of the same work, difference in length and intensity of training, less broad experience. They will discourse at some length whether the job they do is sufficiently worse as to merit the wage differential. Only the physicians are licensed to give prescribe or dispense medications, another sore point.

Similarly with psychologists and psychiatrists here.