retainer vs dental appliance

retainer and dental appliance both are nouns.

Word	Noun	Adjective	Verb	Adverb
retainer	Yes	No	No	No
dental appliance	Yes	No	No	No

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

retainer: a dental appliance that holds teeth (or a prosthesis) in position after orthodontic treatment
dental appliance: a device to repair teeth or replace missing teeth

retainer (noun)	dental appliance (noun)
a dental appliance that holds teeth (or a prosthesis) in position after orthodontic treatment	a device to repair teeth or replace missing teeth
a person working in the service of another (especially in the household)
a fee charged in advance to retain the services of someone