DMD - Doctor of Medicine in Dentristy. So calling any of them "Doctor" is not referring to their profession, but to the degree they've earned. ED - (no, not electile dysfunction) Doctor of Education, PhD - Doctor of Philsophy, DO - Doctor of Osteopathy, DC - Doctor of Chiropractic, JD - Juris Doctorate.
If we wanted to name them after their profession, we'd go "physician", "dentist", "educator", "wingnut elitist", "physician" or "osteopath", "chiropractor", but instead we often use their degree to title them.