house detective vs hotel detective

house detective and hotel detective both are nouns.

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

As nouns, house detective and hotel detective are synonyms defined as:

house detective and hotel detective: a private detective employed by a hotel or retail store

Other synonyms of house detective include house dick.

house detective (noun)	hotel detective (noun)
a private detective employed by a hotel or retail store	a private detective employed by a hotel or retail store