Both degrees use the same curriculum requirements set by the American Dental Association's Commission on Dental Accreditation. Universities have the prerogative to determine what degree is awarded. There is no difference between the two degrees: dentists who have a DMD or DDS (both have same education).
Dentist: A dentist is a person who is qualified as a doctorate in dental surgery (D.D.S.) or dental medicine (D.M.D.), licensed by the state to practice dentistry, and practicing within the scope of that license.
