publishing firm vs publishing house

publishing firm and publishing house both are nouns.

Word	Noun	Adjective	Verb	Adverb
publishing firm	Yes	No	No	No
publishing house	Yes	No	No	No

As nouns, publishing firm and publishing house are synonyms defined as:

Other synonyms of publishing firm include publisher, publishing company.

publishing firm (noun)	publishing house (noun)
a firm in the publishing business	a firm in the publishing business