SAAMI specs are SAAMI specs. There's a max pressure (mean average peak or some such statistical speak) for every "standardized" cartridge.
For some older rounds like the .38 Special, the ammo makers and the ammo buyers wanted to push things a bit farther than the old blackpowder-based pressure standards would allow. The _*modern*_ guns were certainly up to it.
So, they rather cautiously made a new standard something like 1,500 or 2,500 PSI higher than the old, as least for the .38 Special.
SAAMI has a +P spec for 9mm, .38 Special, IIRC .45 ACP, and a few other loads. None for .40 S&W, thank Gawd.
So, you could say it's overpressure, but not enough to cause a problem for modern, high-quality guns made with decent steel.
Don't think there's really a +P+ standard from SAAMI, but some ammo makers have loaded to their own versions of more overpressure than +P for 9mm Para and .38 Special.