What is the difference between a crna and anesthesiologist?

Complex. Anesthesiologist is a doctor who did medical school then residency in anesthesia. Crna is a nurse, experienced in ICU care or similar, who attends an anesthesia training program. In most of the country crna practices under supervision of anesthesiologist, though in some states they can be independent.
Alot. Anesthesiologist is a doctor (an md). Crna us an advance practice nurse who works under the supervision of an anesthesiologist.