If I live in a two-storey home, then my bedroom is upstairs. I might say to a friend that 'I just need to run upstairs to get my coat, and then we can leave for school'
'upstairs' refers to the upper floor of a house or building.
If I am giving someone directions in a building, I might say, " Go down this hall, then up the stairs and turn left. It's on your right."
'up the stairs' is directing someone to actually go up a staircase -'walk up the stairs'.