spelling bee vs contest

spelling bee and contest both are nouns.

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

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

spelling bee: 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 bee include competition.

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