running mate vs campaigner

running mate and campaigner both are nouns.

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

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

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

Other hypernyms of running mate include candidate, nominee.

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