dwelling house vs housing

dwelling house and housing both are nouns.

Word	Noun	Adjective	Verb	Adverb
dwelling house	Yes	No	No	No
housing	Yes	No	No	No

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

Other hypernyms of dwelling house include living accommodations, lodging.

dwelling house (noun)	housing (noun)
housing that someone is living in	structures collectively in which people are housed
	a protective cover designed to contain or support a mechanical component
	stable gear consisting of a decorated covering for a horse, especially (formerly) for a warhorse