32 / 380 PPK have the cowl which holds the barrel to the frame relieved. There is a groove you will find for the recoil spring to sit in.
Putting your PPK slide and spring on a PP frame can result in a serious jam, you can usually force things on but then may never get them off again, due to the missing 1/10 of an inch or so which keeps the spring from binding completely. There is not much space inside the PPK slide for the spring, so this little bit of extra space is critical for the recoil spring to move enough to disassemble the gun.
I have more than a few of these and have played around a fair bit. And yes, I have a PPK that I can't get the slide off of, since the aftermarket recoil spring had one extra winding.
PPK/S is the PP frame, with the PPK cowl design, and the groove, and a PPK slide and recoil spring. The PP has no relief groove, since it's a longer action (barrel/slide/spring) and doesn't need it.