DDS stands for Doctor of Dental Surgery and DMD stands for Dentariae Medicinae Doctorae, which is Latin for Doctor of Dental Medicine. There is no difference between the two degrees.
DDS is the "original" name for the degree and in 1867 Harvard University was the first school to introduce the DMD degree. Harvard names its degrees in Latin. The Latin translation for Doctor of Dental Surgery is Chirurgae Dentium Doctoris, which administrators at Harvard believed would be confusing. So they chose Dentariae Medicinae Doctorae (DMD) instead, which translates to Doctor of Dental Medicine. Over the last 150-odd years, some other schools followed in Harvard's footsteps.
Popularity of the degrees
There are around 60 schools in the United States that offer degrees in dentistry. Of these, about 60% offer the DDS degree while 40% name their degree DMD. Other than the name, there is no difference in the academic training required to become a dentist from any of these schools. All dental schools in the U.S. are required to follow the curriculum set by the American Dental Association. All dentists, whether DMD or DDS, must meet the same national and regional certification standards in order to practice.
Qualifications of a Dentist
After 3 or more years of undergraduate education, students must attend dental school for 4 years in order to graduate and become a general dentist. Dental specialists, such as orthodontists, periodontists, and oral and maxillofacial surgeons require additional post-graduate training. Before they are allowed to practice, all dentists are required to also pass a national written exam and a state or regional clinical licensing exam.
All dentists must meet continuing education requirements throughout their careers in order to retain their license to practice dentistry. This allows them to stay abreast of the latest scientific thinking and developments in clinical guidelines.