I have some of the original Winchester Treasury Load +P+ ammunition, with the LEO warning on the boxes. That brass is definitely thicker and feels more like .357 Magnum brass when sized. It's all nickle plated.
Some +P brass is also thicker, in particular some from Winchester and Speer. You can feel it when you size it. Of course, the older PMC .38 brass was also thicker when it was made in Boulder City, NV. I don't know what the brass is like since the company was purchased by the Korean company and moved there.
Hope this helps.
Fred
PS: I'm going to have to find a machinist with a ball end micrometer and actually measure the wall thickness of various brands of brass. My dial caliper and micrometer won't do it, since you have to measure beyond the case mouth to get away from crimp/flaring variables.