competition vs rivalry

competition and rivalry both are nouns.

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

As nouns, competition and rivalry are synonyms defined as:

Other synonyms of competition include contention.

competition (noun)	rivalry (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