spelling bee vs spelling contest

spelling bee and spelling contest both are nouns.

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

As nouns, spelling bee and spelling contest are synonyms defined as:

spelling bee and spelling contest: a contest in which you are eliminated if you fail to spell a word correctly

Other synonyms of spelling bee include spelldown.

spelling bee (noun)	spelling contest (noun)
a contest in which you are eliminated if you fail to spell a word correctly	a contest in which you are eliminated if you fail to spell a word correctly