There is no difference between the POST-WAR P-38 and the P1.
The P1 is simply the P-38 marked for use by the German government.
After the war Germany wanted to adopt the P-38, but also wanted a clean break with the Nazi past. They decided to start a new numbering system for small arms. The first pistol adopted was a slightly redesigned P-38 made with an aluminum frame, and named the "P1".
Walther guns made for export and civilian sales were still marked "P-38".
Other then the marks, they are exactly the same guns, produced on the same production lines.
The later P4 is a redesigned P-38/P1. The German police were starting a search for a new service pistol, but Walther didn't have their new designs ready. So, Walther did a partial rework of the P-38/P1 to fill in until the P5 was ready.
The P4 has a solid slide top, no loaded chamber pin, a modified firing pin and hammer, and the safety was changed to a spring-loaded de-cocker.
As soon as Walther got the new P5 ready, the P4 was discontinued. The Walther P5 is also largely a redesigned P-38.
The Current batch of P1's are a great buy. A few years ago the same guns with the P-38 marks were selling in the $400.00 and up range. In a few more years, these P1's will be selling for much more than the current price.
These P1's are reasonably accurate, reliable with FMJ ammo, often reliable with Hollow-point ammo, and very high quality.
BUY ONE, you'll be sorry if you don't.