contest vs dispute

contest and dispute both are nouns.

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

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

Other hyponyms of contest include challenge, gainsay.

contest (noun)	dispute (noun)
a struggle between rivals	coming into conflict with
an occasion on which a winner is selected from among two or more contestants	a disagreement or argument about something important

contest (verb)	dispute (verb)
to make the subject of dispute, contention, or litigation	take exception to
	have a disagreement over something