central office vs home office

central office and home office both are nouns.

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

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

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

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

central office (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