Yes, that barrel marking is confusing. The PP was originally marked "Police Positive .38" but when it was upsized and chambered for the .38 Special, it was marked "Police Positive 38 Special" in such a way that the "Special" seems to apply to the gun and not to the cartridge. (It was also chambered for the .32-20, in which case the word "Special" came before the ".32 WCF", making it sort of clear that the word referred to the gun also.)
Anyway, FWIW, the word "Positive" refers to Colt's positive safety lock (hammer block) which was a big selling point since at that time S&W's hammer block was spring operated and not "positive". (That was the type that failed and led to the "positive" design S&W still uses.)
Jim