orthodontics vs dentistry

orthodontics and dentistry both are nouns.

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

As nouns, dentistry is a hypernym of orthodontics; that is, dentistry 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
dentistry: the branch of medicine dealing with the anatomy and development and diseases of the teeth

Other hypernyms of orthodontics include dental medicine, odontology.

orthodontics (noun)	dentistry (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