contention vs contest

contention and contest both are nouns.

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

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

contention (noun)	contest (noun)
the act of competing as for profit or a prize	a struggle between rivals
a contentious speech act; a dispute where there is strong disagreement	an occasion on which a winner is selected from among two or more contestants
a point asserted as part of an argument

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