^^^ In addition to what Dave T wrote, the boxes for most +P+ loads bore disclaimers stating "This Ammunition Should Only be Fired in .357 Magnum Revolvers"
or something similar. The should be your first clue as to what the pressures may have been.
It also helps explain the thicker-than-normal brass.
.38Spl+P+ was marketed to LE agencies essentially as a sham to allow officers (and sometimes security guards) to carry ammo with performance comparable to .357Mag without running afoul of PR-motivated laws and policies prohibiting the use of so-called "super-lethal" Magnum ammo.
AFAIK no verifiable standard for +P+ rounds ever existed; it varied by manufacturer and load.
+P+ has been largely dropped from commercial production because (a) prosecutors, city managers, etc. figured the sham out, (b) the stellar street performance of 125gr .357Mag JHP loads prompted many LE agencies to drop the pretense, and (c) most LE agencies have switched to autoloaders.