home office vs central office

home office and central office both are nouns.

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

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

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

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

home office (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