on a lower floor vs down the stairs

on a lower floor and down the stairs both are adverbs.

Word	Noun	Adjective	Verb	Adverb
on a lower floor	No	No	No	Yes
down the stairs	No	No	No	Yes

As adverbs, on a lower floor and down the stairs are synonyms defined as:

Other synonyms of on a lower floor include below, downstairs.

on a lower floor (adverb)	down the stairs (adverb)
on a floor below	on a floor below