pseudonym vs stage name

pseudonym and stage name both are nouns.

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

As nouns, stage name is a hyponym of pseudonym; that is, stage name is a word with a more specific, narrower meaning than pseudonym:

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

Other hyponyms of pseudonym include nom de plume, pen name, hagionym.

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