nominee vs running mate

nominee and running mate both are nouns.

Word	Noun	Adjective	Verb	Adverb
nominee	Yes	No	No	No
running mate	Yes	No	No	No

As nouns, running mate is a hyponym of nominee; that is, running mate is a word with a more specific, narrower meaning than nominee:

nominee: a politician who is running for public office
running mate: a nominee for the lesser of two closely related political offices

Other hyponyms of nominee include dark horse, favorite son, spoiler, stalking-horse, write-in, write-in candidate.

nominee (noun)	running mate (noun)
a politician who is running for public office	a nominee for the lesser of two closely related political offices