rival vs favorite

rival and favorite both are nouns.

Word	Noun	Adjective	Verb	Adverb
rival	Yes	Yes	Yes	No
favorite	Yes	Yes	Yes	No

As nouns, favorite is a hyponym of rival; that is, favorite is a word with a more specific, narrower meaning than rival:

rival (noun)	favorite (noun)
the contestant you hope to defeat	something regarded with special favor or liking
	a special loved one
	a competitor thought likely to win

rival (adjective)	favorite (adjective)
as a rival in a competition	preferred above all others and treated with partiality
	appealing to the general public

rival (verb)	favorite (verb)
be the rival of, be in competition with	To mark an item as a personal favorite on social media
be equal to in quality or ability