housing vs lodging

housing and lodging both are nouns.

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

As nouns, housing and lodging are synonyms defined as:

Other synonyms of housing include living accommodations.

housing (noun)	lodging (noun)
structures collectively in which people are housed	the act of lodging
a protective cover designed to contain or support a mechanical component	structures collectively in which people are housed
stable gear consisting of a decorated covering for a horse, especially (formerly) for a warhorse	the state or quality of being lodged or fixed even temporarily