pen name vs pseudonym

pen name and pseudonym both are nouns.

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

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

pen name: an author's pseudonym
pseudonym: a fictitious name used when the person performs a particular social role

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

pen name (noun)	pseudonym (noun)
an author's pseudonym	a fictitious name used when the person performs a particular social role