home base vs home office

home base and home office both are nouns.

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

As nouns, home base and home office are synonyms defined as:

home base and home office: (usually plural) the office that serves as the administrative center of an enterprise

Other synonyms of home base include central office, headquarters, main office.

home base (noun)	home office (noun)
(usually plural) the office that serves as the administrative center of an enterprise	(usually plural) the office that serves as the administrative center of an enterprise
(baseball) base consisting of a rubber slab where the batter stands; it must be touched by a base runner in order to score