house of prostitution vs brothel

house of prostitution and brothel both are nouns.

Word	Noun	Adjective	Verb	Adverb
house of prostitution	Yes	No	No	No
brothel	Yes	No	No	No

As nouns, house of prostitution and brothel are synonyms defined as:

house of prostitution and brothel: a building where prostitutes are available

Other synonyms of house of prostitution include bagnio, bawdyhouse, bordello, cathouse, house of ill repute, sporting house, whorehouse.

house of prostitution (noun)	brothel (noun)
a building where prostitutes are available	a building where prostitutes are available