Hello qaija!
I've explained this in somewhat basic terms, if you're interested in the exact details I'd recommend checking out
this section of the Wiki's Mines page.
There are four ways of opening a way down to the next floor:
Staircases – Once you've reached Level 2 in the Mining skill, you'll be able to craft Staircases for 99 Stone each. These place a Ladder ("grid") right in front of your farmer, allowing rapid, predictable and safe descent. With the downside, of course, that they cost 99 Stone per!
Breakin' Rocks – It is guaranteed that if you break all the rocks/nodes on a floor, you'll get a Ladder. Often you'll get it much sooner then that (as I'm sure you've noticed by now), but as soon as you get one, rocks will no longer have that chance.
On Generation – When the game loads a floor, it will occasionally spawn a Ladder out in the open for you. So if you find it, great! That's lots of time saved. But since the game's already generated a ladder for you, rocks won't drop them, meaning that if you don't spot that ladder, you'll be wasting time mining rocks when they can't even help you.
From Monsters – Every monster you defeat will have a 15% chance of "dropping" a ladder on the ground. These ladders don't stop rocks – or other monsters – from dropping ladders, though, so even if you get one (or multiple) from this way, you could still get more from rocks and/or monsters. And even if you've already uncovered a ladder through any of the 3 above methods, monsters can still drop them. So they're pretty much a different system, which is why confusion can arise, as it has here. :D
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And to answer your actual question, no, there is zero difference between all these ladders, they
all take you down
exactly one floor, 100% of the time.
Hope this helps!