home office vs business office

home office and business office both are nouns.

Word	Noun	Adjective	Verb	Adverb
home office	Yes	No	No	No
business office	Yes	No	No	No

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

home office: (usually plural) the office that serves as the administrative center of an enterprise
business office: place of business where professional or clerical duties are performed

Other hypernyms of home office include office.

home office (noun)	business office (noun)
(usually plural) the office that serves as the administrative center of an enterprise	place of business where professional or clerical duties are performed