lodging vs lodgment

lodging and lodgment both are nouns.

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

As nouns, lodging and lodgment are synonyms defined as:

lodging and lodgment: the state or quality of being lodged or fixed even temporarily

Other synonyms of lodging include lodgement.

lodging (noun)	lodgment (noun)
the act of lodging	the state or quality of being lodged or fixed even temporarily
structures collectively in which people are housed
the state or quality of being lodged or fixed even temporarily