periodontics vs odontology

periodontics and odontology both are nouns.

Word	Noun	Adjective	Verb	Adverb
periodontics	Yes	No	No	No
odontology	Yes	No	No	No

As nouns, odontology is a hypernym of periodontics; that is, odontology is a word with a broader meaning than periodontics:

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

Other hypernyms of periodontics include dental medicine, dentistry.

periodontics (noun)	odontology (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