upstairs vs up the stairs

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

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

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

Other synonyms of upstairs include on a higher floor.

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

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

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