on a higher floor vs up the stairs

on a higher floor and up the stairs both are adverbs.

Word	Noun	Adjective	Verb	Adverb
on a higher floor	No	No	No	Yes
up the stairs	No	No	No	Yes

As adverbs, on a higher floor and up the stairs are synonyms defined as:

Other synonyms of on a higher floor include upstairs.

on a higher floor (adverb)	up the stairs (adverb)
on a floor above	on a floor above