competition vs contest

competition and contest both are nouns.

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

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

As nouns, competition and contest are synonyms defined as:

competition and contest: an occasion on which a winner is selected from among two or more contestants

competition (noun)	contest (noun)
the act of competing as for profit or a prize	a struggle between rivals
an occasion on which a winner is selected from among two or more contestants	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

competition (verb)	contest (verb)
	to make the subject of dispute, contention, or litigation