fame vs celebrity

fame and celebrity both are nouns.

Word	Noun	Adjective	Verb	Adverb
fame	Yes	No	No	No
celebrity	Yes	No	No	No

As nouns, fame and celebrity are synonyms defined as:

fame and celebrity: the state or quality of being widely honored and acclaimed

Other synonyms of fame include renown.

fame (noun)	celebrity (noun)
the state or quality of being widely honored and acclaimed	a widely known person
favorable public reputation	the state or quality of being widely honored and acclaimed