stage name vs pseudonym

stage name and pseudonym both are nouns.

Word	Noun	Adjective	Verb	Adverb
stage name	Yes	No	No	No
pseudonym	Yes	No	No	No

As nouns, pseudonym is a hypernym of stage name; that is, pseudonym is a word with a broader meaning than stage name:

stage name: the pseudonym of an actor
pseudonym: a fictitious name used when the person performs a particular social role

Other hypernyms of stage name include anonym, nom de guerre.

stage name (noun)	pseudonym (noun)
the pseudonym of an actor	a fictitious name used when the person performs a particular social role