consulting firm vs consulting company

consulting firm and consulting company both are nouns.

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

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

consulting firm and consulting company: a firm of experts providing professional advice to an organization for a fee

consulting firm (noun)	consulting company (noun)
a firm of experts providing professional advice to an organization for a fee	a firm of experts providing professional advice to an organization for a fee