Yes. Lets see if I can make an ASCII rendition that renders correctly. `-` is level floor, `v` is a down stair, `x` is an up/down stair and `^` is an up stair. The simplest possible stair connection between layers is a down stair above with an up stair below:

    ---v---
    ---^---

To make a very tall staircase, you can either stack pairs of stairs next to each other (this approach actually has some gameplay benefits, but isn't usually necessary):

    ---v-----
    ---^v----
    ----^v---
    -----^---

Or, you can use up/down stairs, which are a single block that acts as both an up and a down stair:

    ---v---
    ---x---
    ---x---
    ---^---

In the ASCII game, you had to place all of these manually, so you were in full control. In the new Steam game, it's my understanding that you just select the top and bottom layers for your staircase and it automatically builds the "right" stair types for you. The problem I have seen reported is that sometimes it will erroneously designate something like this:

    ---v---
    ---v---
    ---x---
    ---^---

This staircase does not allow dwarves to transit from layer 2 up to layer 1, and permanently removes material, meaning it's not possible to completely fix the mistake.

Relative to a particular floor, there are stairs that go up to the floor above and there are stairs that go down to the floor below.