What are the differences between a PPK and PPK/S?

The PPK/s was developed to allow Walther to import the smaller PP guns into the US after the Gun Control Act of 1968.

The PPK was about 1/4" too short in the butt to meet the requirement, so Walther basically fitted a PPK slide to the longer butted PP model.

The basic differences between the PPK and the PPK/s are, the PPK/s has a solid steel backstrap, with a slightly longer butt.
The PPK has a shorter "skeleton" butt which has no actual backstrap.  Instead, the grips wrap around the back of the frame, forming the grip.

The PPK/s has panel-type plastic grips with an exposed steel frame all around.

The PPK/s holds one more round in it's magazine.