HQ vs general headquarters

HQ and general headquarters both are nouns.

Word	Noun	Adjective	Verb	Adverb
HQ	Yes	No	No	No
general headquarters	Yes	No	No	No

As nouns, general headquarters is a hyponym of HQ; that is, general headquarters is a word with a more specific, narrower meaning than HQ:

HQ: the military installation from which a commander performs the functions of command
general headquarters: military headquarters from which a military commander controls and organizes the forces

Other hyponyms of HQ include command post, GHQ, guardhouse.

HQ (noun)	general headquarters (noun)
the military installation from which a commander performs the functions of command	military headquarters from which a military commander controls and organizes the forces