Also, the .357 is a physically longer cartridge. You can load a .357 revolver with .38 cartridges (or .38+P), but not the other way around. (But you probably already knew that.)
Basically years back when I first saw the .38 plus p I bought a box. There were 20 or 25 to the box. The salesman told me to be careful as most .38 specials may not be able to handle the load. I went home and loaded my .357 king cobra with the 38 plus p and some .357 semi wad cutter rounds. The kind of box you buy for target and they come 100 to the box instead of fifty. I alternated the rounds and fired the weapon and there was not much difference if any in the recoil. Not very scientific I know. I do have some .357 plus p rounds but i knew there would be no sense in trying to compare the two.