peppermint vs mint candy

peppermint and mint candy both are nouns.

Word	Noun	Adjective	Verb	Adverb
peppermint	Yes	No	No	No
mint candy	Yes	No	No	No

As nouns, mint candy is a hypernym of peppermint; that is, mint candy is a word with a broader meaning than peppermint:

Other hypernyms of peppermint include mint.

peppermint (noun)	mint candy (noun)
a candy flavored with peppermint oil	a candy that is flavored with a mint oil
herb with downy leaves and small purple or white flowers that yields a pungent oil used as a flavoring
red gum tree of Tasmania