peppermint vs peppermint gum

peppermint and peppermint gum both are nouns.

Word	Noun	Adjective	Verb	Adverb
peppermint	Yes	No	No	No
peppermint gum	Yes	No	No	No

As nouns, peppermint and peppermint gum are synonyms defined as:

Other synonyms of peppermint include Eucalyptus amygdalina, red gum.

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