periodontia vs dental medicine

periodontia and dental medicine both are nouns.

Word	Noun	Adjective	Verb	Adverb
periodontia	Yes	No	No	No
dental medicine	Yes	No	No	No

As nouns, dental medicine is a hypernym of periodontia; that is, dental medicine is a word with a broader meaning than periodontia:

periodontia: the branch of dentistry dealing with diseases of the gums and other structures around the teeth
dental medicine: the branch of medicine dealing with the anatomy and development and diseases of the teeth

Other hypernyms of periodontia include dentistry, odontology.

periodontia (noun)	dental medicine (noun)
the branch of dentistry dealing with diseases of the gums and other structures around the teeth	the branch of medicine dealing with the anatomy and development and diseases of the teeth