running mate vs nominee

running mate and nominee both are nouns.

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

As nouns, nominee is a hypernym of running mate; that is, nominee is a word with a broader meaning than running mate:

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

Other hypernyms of running mate include campaigner, candidate.

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