Basically, the stampings on the slide are the only difference.
The WWII Nazi P-38 had a steel frame.
The POST-WAR Walther P-38/P1 had an aluminum frame.
The post-war P-38 was the commercial version sold to police, foreign military contracts, and commercial sales.
The P1 is basically the P-38 only marked for use by the West German military who had designated it as the "Pistole One", or P1.
Later P1's had some minor improvements like a reinforcing pin through the frame to provide a "wear seat" for the locking block.
As for the rest, the guns are 100% interchangeable because they are the same gun.
This is no different then the US 1911-A1 pistol, and the Colt Government Model.
One is military issue, the other was the commercial version.