house detective vs operative

house detective and operative both are nouns.

Word	Noun	Adjective	Verb	Adverb
house detective	Yes	No	No	No
operative	Yes	Yes	No	No

As nouns, operative is a hypernym of house detective; that is, operative is a word with a broader meaning than house detective:

house detective: a private detective employed by a hotel or retail store
operative: someone who can be employed as a detective to collect information and assist in criminal investigations

Other hypernyms of house detective include PI, private detective, private eye, private investigator, shamus, sherlock.

house detective (noun)	operative (noun)
a private detective employed by a hotel or retail store	someone who can be employed as a detective to collect information and assist in criminal investigations
	a person secretly employed in espionage for a government

house detective (adjective)	operative (adjective)
	being in force or having or exerting force
	relating to or requiring or amenable to treatment by surgery especially as opposed to medicine
	(of e.g. a machine) performing or capable of performing
	effective; producing a desired effect