orthodontics vs odontology

orthodontics and odontology both are nouns.

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

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

orthodontics: the branch of dentistry dealing with the prevention or correction of irregularities of the teeth
odontology: the branch of medicine dealing with the anatomy and development and diseases of the teeth

Other hypernyms of orthodontics include dental medicine, dentistry.

orthodontics (noun)	odontology (noun)
the branch of dentistry dealing with the prevention or correction of irregularities of the teeth	the branch of medicine dealing with the anatomy and development and diseases of the teeth