Stairs Can't Intersect With Walls

Stairs need at least 1 tile of space in front of them. In your original build, you have enough space between the wall and the stairs. In your new build, you are putting your stairs right up against the wall on the first level, which is fine -- but in order for them to be usable to get to the second level, they need that same space (flooring) at the top.

Basically you're not building exactly the same thing. Those black stairs don't have a tile of space at the top, so they can't be placed. You need to put in a room that adds the extra tiles of flooring needed at the top of those stairs. Like this:

And the upper level looks like this:

These stairs aren't usable, if I try to drag them to make them wider, that's when I get the error "cannot intersect with walls". That's because they need the extra tile space, so here's how you fix it:

I put in a "Flat Square" (under the Walls & Empty Rooms tab in build mode) over top the stairs to add that extra flooring, and voila:

How it looks from the inside (looks like what you are trying to achieve from your original build):