contest vs oppose

contest is a noun but oppose is not a noun.

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

As verbs, oppose is a hypernym of contest; that is, oppose is a word with a broader meaning than contest:

contest (noun)	oppose (noun)
a struggle between rivals
an occasion on which a winner is selected from among two or more contestants

contest (verb)	oppose (verb)
to make the subject of dispute, contention, or litigation	be resistant to
	be against; express opposition to
	set into opposition or rivalry
	fight against or resist strongly
	act against or in opposition to
	contrast with equal weight or force