A dermatologist is a medical doctor who specializes in the diagnosis and treatment of skin, hair, and nail conditions. They have completed an undergraduate degree, medical school, and a dermatology residency program. They are licensed to practice medicine and are able to diagnose and treat medical conditions, including skin cancer, as well as perform surgical procedures such as mole removal.

On the other hand, a cosmetologist is a professional who has been trained in the beauty industry. They focus on the beauty and aesthetic aspects of hair, skin and nails. They typically complete a cosmetology program and are licensed to provide services such as haircuts, hairstyling, coloring, facials, and makeup application. They can not diagnose or treat medical conditions, and they don't have the same level of medical training as dermatologists.

In summary, a dermatologist is a medical doctor who specializes in skin, hair, and nail conditions, while a cosmetologist is a beauty professional who provides hair, skin, and nail services.