foe vs rival

foe and rival both are nouns.

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

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

Other hypernyms of foe include challenger, competition, competitor, contender.

foe (noun)	rival (noun)
a personal enemy	the contestant you hope to defeat
an armed adversary (especially a member of an opposing military force)

foe (adjective)	rival (adjective)
	as a rival in a competition

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