central office vs home base

central office and home base both are nouns.

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

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

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

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

central office (noun)	home base (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