Could be any of the above; it's never confirmed.
The only mechanical description we get1 is in Philosopher's Stone, which is unhelpfully vague (emphasis mine):
There were a hundred and forty-two staircases at Hogwarts: wide, sweeping ones; narrow, rickety ones; some that led somewhere different on a Friday; some with a vanishing step halfway up that you had to remember to jump. Then there were doors that wouldn't open unless you asked politely, or tickled them in exactly the right place, and doors that weren't really doors at all, but solid walls just pretending. It was also very hard to remember where anything was, because it all seemed to move around a lot.
Harry Potter and the Philosopher's Stone Chapter 8: "The Potions Master"
The only other specific mention of the moving staircases, that I know of, is from a 2000 live chat on Scholastic.com, where Rowling just says that they do move (bold is my emphasis, italic is from the source):
Do you have an actual floorplan for Hogwarts? Do you use it when writing the books?
A. I haven't drawn it, because it would be difficult for the most skilled architect to draw, owing to the fact that the staircases and the rooms keep moving. However, I have a very vivid mental image of what it looks like.
There is one reference to a "swivelling staircase":
"You can't come down here!" Ginny was calling to the crowd. "No, sorry, you're going to have to go round by the swivelling staircase, someone's let off Garrotting Gas just along here -"
Harry Potter and the Order of the Phoenix Chapter 32: "Out of the Fire"
Which presumably moves in some physical way, going by the name, though whether it changes destination or just swivels on the spot (like Dumbledore's stairs) is unknown.
Feel free to headcanon, to your heart's content.
1 Aside from the stairs to Dumbledore's office, which are a bit unique