contestation vs dispute

contestation and dispute both are nouns.

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

As nouns, dispute is a hypernym of contestation; that is, dispute is a word with a broader meaning than contestation:

contestation: a contentious speech act; a dispute where there is strong disagreement
dispute: a disagreement or argument about something important

Other hypernyms of contestation include conflict, difference, difference of opinion.

contestation (noun)	dispute (noun)
a contentious speech act; a dispute where there is strong disagreement	coming into conflict with
	a disagreement or argument about something important

contestation (verb)	dispute (verb)
	take exception to
	have a disagreement over something