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.
Walther did change the firing pin design sometime after they restarted production in the late 50's so they wont interchange. Neither the P.38 or P.1 is "rated" for +P ammo. And there have been instances reported on the boards of both slide and frame cracking for both models. I wouldn't recommend shooting any Aluminum frame pistol with +P ammo.
The P-38 cannot take the .22 conversion unit for the P-1. Forget exactly why, but when
I spoke to the importer (Earl's?) a few years ago when I told him my pistol was a Wehrmacht one he said the conversion unit wouldn't fit.