spelling bee vs competition

spelling bee and competition both are nouns.

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

As nouns, competition is a hypernym of spelling bee; that is, competition 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
competition: an occasion on which a winner is selected from among two or more contestants

Other hypernyms of spelling bee include contest.

spelling bee (noun)	competition (noun)
a contest in which you are eliminated if you fail to spell a word correctly	the act of competing as for profit or a prize
	an occasion on which a winner is selected from among two or more contestants
	the contestant you hope to defeat
	a business relation in which two parties compete to gain customers