publishing firm vs publishing company

publishing firm and publishing company both are nouns.

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

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

publishing firm and publishing company: a firm in the publishing business

Other synonyms of publishing firm include publisher, publishing house.

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