up the stairs vs on a higher floor

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

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

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

Other synonyms of up the stairs include upstairs.

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