home base vs business office

home base and business office both are nouns.

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

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

home base: (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 base include office.

home base (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
(baseball) base consisting of a rubber slab where the batter stands; it must be touched by a base runner in order to score