Basically the post-war aluminum frame P-38 was made for commercial sales, foreign military and police contracts, and for the West German police.
The P1 was nothing more then the P-38 as marked for the West German military.
The post-war West German military liked the P-38 and wanted to use it.
As a break with the Nazi past, they started using new designations for firearms. The first pistol they adopted was known as the Pistole One or P1.
Other than that, the two guns are exactly the same and use the same parts. The early post-war P-38 and P1 are exactly the same except for markings.
Later, the P1 was given some upgrade changes like a bolt through the frame to give the locking block a steel surface to operate on because the aluminum frame operating ramp wore in high round count guns and started giving locking problems.
The slide and frame was also slightly beefed up to prevent cracking when used heavily.
Other than those few changes, all other parts are the same.