home office vs home base

home office and home base both are nouns.

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

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

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

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

home 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