housing vs living accommodations

housing and living accommodations both are nouns.

Word	Noun	Adjective	Verb	Adverb
housing	Yes	No	No	No
living accommodations	Yes	No	No	No

As nouns, housing and living accommodations are synonyms defined as:

housing and living accommodations: structures collectively in which people are housed

Other synonyms of housing include lodging.

housing (noun)	living accommodations (noun)
structures collectively in which people are housed	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