law firm vs business firm

law firm and business firm both are nouns.

Word	Noun	Adjective	Verb	Adverb
law firm	Yes	No	No	No
business firm	Yes	No	No	No

As nouns, business firm is a hypernym of law firm; that is, business firm is a word with a broader meaning than law firm:

law firm: a firm of lawyers
business firm: the members of a business organization that owns or operates one or more establishments

Other hypernyms of law firm include firm, house.

law firm (noun)	business firm (noun)
a firm of lawyers	the members of a business organization that owns or operates one or more establishments