candidacy vs political campaign

candidacy and political campaign both are nouns.

Word	Noun	Adjective	Verb	Adverb
candidacy	Yes	No	No	No
political campaign	Yes	No	No	No

As nouns, candidacy and political campaign are synonyms defined as:

candidacy and political campaign: the campaign of a candidate to be elected

Other synonyms of candidacy include campaigning, candidature, electioneering.

candidacy (noun)	political campaign (noun)
the campaign of a candidate to be elected	the campaign of a candidate to be elected
	a race between candidates for elective office