lodging vs housing

lodging and housing both are nouns.

Word	Noun	Adjective	Verb	Adverb
lodging	Yes	No	No	No
housing	Yes	No	No	No

As nouns, lodging and housing are synonyms defined as:

Other synonyms of lodging include living accommodations.

lodging (noun)	housing (noun)
the act of lodging	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
the state or quality of being lodged or fixed even temporarily	stable gear consisting of a decorated covering for a horse, especially (formerly) for a warhorse