second best vs rival

second best and rival both are nouns.

Word	Noun	Adjective	Verb	Adverb
second best	Yes	No	No	No
rival	Yes	Yes	Yes	No

As nouns, rival is a hypernym of second best; that is, rival is a word with a broader meaning than second best:

Other hypernyms of second best include challenger, competition, competitor, contender.

second best (noun)	rival (noun)
the competitor who finishes second	the contestant you hope to defeat

second best (adjective)	rival (adjective)
	as a rival in a competition

second best (verb)	rival (verb)
	be the rival of, be in competition with
	be equal to in quality or ability