What’s the difference between a DMD and DDS Degree? Other than the spelling… nothing!
In the United States the Doctor of Dental Surgery and Doctor of Dental Medicine are both professional degrees which qualify a dentist for licensing. The DDS and DMD degrees are considered equivalent by the American Dental Association. 
The DDS degree came first, being offered originally by the Baltimore College of Dental Surgery in 1840. Harvard University was the first dental school to award the DMD degree in 1867. Harvard only grants degrees in Latin, and the Latin translation of Doctor of Dental Surgery, “Chirurgiae Dentium Doctoris”, did not share the “DDS” initials of the English term. “The degree ‘Scientiae Dentium Doctoris’, which would leave the initials of DDS unchanged, was then considered, but was rejected on the ground that dentistry was not a science.” A Latin scholar was consulted. It was finally decided that “Medicinae Doctoris” be modified with “Dentariae”. This is how the DMD, or “Doctor Medicinae Dentariae” degree, was started. The assertion that “dentistry was not a science” reflected the view that dental surgery was an art informed by science, not a science per se—notwithstanding that the scientific component of dentistry is today recognized in the Doctor of Dental Science (DDSc) degree.
Other dental schools made the switch to this notation, and in 1989, 23 of the 66 North American dental schools awarded the DMD. There is no meaningful difference between the DMD and DDS degrees, and all dentists must meet the same national and regional certification standards in order to practice.
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1. “DDS/DMD” Archived 17 September 2010 at the Wayback Machine, American Dental Association
2. Ring ME. (2005). “Founders of a profession: the original subscribers to the first dental journal in the world”. J Am Coll Dent. 72 (2): 20–5. PMID 16350927.
3. “DMD Program”. Ohsu.edu. Retrieved 23 January 2017.
4. Koch, Charles R.E.; et al. (1910), History of Dental Surgery: History of the development of dentistry, operative dentistry, prosthetic dentistry, orthodontia, oral surgery, dental literature, dental journalism, dental education and dental colleges, 1, National Art Publishing Company, p. 463, LCCN 09017597.
5. “Public perception of DDS versus DMD degrees.” Journal of the American College of Dentists. 1999. Fall; 66(3):29-37. Lalumandier, JA.