spelling contest vs contest

spelling contest and contest both are nouns.

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

As nouns, contest is a hypernym of spelling contest; that is, contest is a word with a broader meaning than spelling contest:

spelling contest: a contest in which you are eliminated if you fail to spell a word correctly
contest: an occasion on which a winner is selected from among two or more contestants

Other hypernyms of spelling contest include competition.

spelling contest (noun)	contest (noun)
a contest in which you are eliminated if you fail to spell a word correctly	a struggle between rivals
	an occasion on which a winner is selected from among two or more contestants

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