up the stairs vs upstairs

up the stairs is not a noun while upstairs is a noun.

Word	Noun	Adjective	Verb	Adverb
up the stairs	No	No	No	Yes
upstairs	Yes	Yes	No	Yes

As adverbs, up the stairs and upstairs are synonyms defined as:

Other synonyms of up the stairs include on a higher floor.

up the stairs (noun)	upstairs (noun)
	the part of a building above the ground floor

up the stairs (adjective)	upstairs (adjective)
	on or of upper floors of a building

up the stairs (adverb)	upstairs (adverb)
on a floor above	on a floor above
	with respect to the mind