central office vs headquarters

central office and headquarters both are nouns.

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

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

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

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

central office (noun)	headquarters (noun)
(usually plural) the office that serves as the administrative center of an enterprise	the military installation from which a commander performs the functions of command
	(usually plural) the office that serves as the administrative center of an enterprise
	(plural) a military unit consisting of a commander and the headquarters staff