I don't know what a PPK-s1 is. A PPK is the original model and in the late sixties, to be able to imprt it into the US, they came up with the PPK/S. It's (I believe this is straight) a PPK slide and a PP frame. A PPK/S basically has a slightly larger grip and holds one more in the mag. A lot of people find them a bit more comfortable because of the larger grip. I'm strange and have small hands so I prefer the PPK.
If I'm wrong about something someone will correct me.