rivalry vs competition

rivalry and competition both are nouns.

Word	Noun	Adjective	Verb	Adverb
rivalry	Yes	No	No	No
competition	Yes	No	No	No

As nouns, rivalry and competition are synonyms defined as:

Other synonyms of rivalry include contention.

rivalry (noun)	competition (noun)
the act of competing as for profit or a prize	the act of competing as for profit or a prize
	an occasion on which a winner is selected from among two or more contestants
	the contestant you hope to defeat
	a business relation in which two parties compete to gain customers