pen name vs nom de guerre

pen name and nom de guerre both are nouns.

Word	Noun	Adjective	Verb	Adverb
pen name	Yes	No	No	No
nom de guerre	Yes	No	No	No

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

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

Other hypernyms of pen name include anonym, pseudonym.

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