home base vs central office

home base and central office both are nouns.

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

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

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

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

home base (noun)	central 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