runner-up vs rival

runner-up and rival both are nouns.

Word	Noun	Adjective	Verb	Adverb
runner-up	Yes	No	No	No
rival	Yes	Yes	Yes	No

As nouns, rival is a hypernym of runner-up; that is, rival is a word with a broader meaning than runner-up:

Other hypernyms of runner-up include challenger, competition, competitor, contender.

runner-up (noun)	rival (noun)
the competitor who finishes second	the contestant you hope to defeat

runner-up (adjective)	rival (adjective)
	as a rival in a competition

runner-up (verb)	rival (verb)
	be the rival of, be in competition with
	be equal to in quality or ability