Yes, there is a difference:
Cooper Puncture Test - YouTube
I have been running exclusively AT tires for a decade.
The more serious duty offroad tires have extra plies and stronger carcass plus the deep tread. Since they are usually LTE, the plies are thicker, too. This does not make them invincible but should be better even on road. Most AT tires don't qualify for that description though.
So that's the principle. My experience is just an anecdote but it does conform to expectations.
I had 1 flat on Geolander AT-S on my Outback. I picked up a monster drill bit in town.
Later, I had 1 flat on a Continental AT when I was running two sets (the other was KO2). This was from a box cutter. I was very disappointed at this one though for me the set was for street and easy dirt only anyway.
The drill that got into the ATS was quite something. No issues with the KO2, with Toyo ATII, or, so far, with ATZ P3.
The interesting part was the SL AT3W on the 4Runner. Plenty of use in all sorts of conditions with 3 punctures in one and the same part of AZ. No issues in town, UT, or MT, or elsewhere in AZ, not even at lower tread. But three punctures in particularly sharp rocks to the west towards CA, both north and south of I-10.
Finally, the tires listed together are not in the same league construction wise.
ATZ P3/ST Maxx, Toyo CT, KO2 are AT tires that are as tough as MT tires because of the 3 vs 2 ply carcass. On top of those you get the steel and then nylon/poly-amid.
Toyo AT II fits either above or below, depending on size. Not sure about the AT III.
Wildpeaks, 265 70 17 LTE Toyo AT II have at least something extra. Like the Wildpeak has wider steel belts. That size AT II had an extra nylon ply.
Most ATs have no distinctive features (and the Duratracs have 4 tread plies total! vs 5 to 6 for all others) and so the tread depth and the more material in LT tires would be the only difference vs regular tires.