The Police Positive had a shorter frame and cylinder then the Police Positive Special.
The Police Positive was offered in either .32 Colt New Police (same as .32 S&W Long) or .38 Colt New Police (same as .38 S&W).
The Police Positive Special was offered in .32-20 WCF and .38 Special during the time period under question. Both were offered in .22 rimfire, but again that's a moot point here.
The Police Positive .32 and .38 were not always in the same serial number series. The Police Positive Special was in its own series. All were different.
To find out who is on first, it's necessary to determine if we are discussing a Police Positive chambered in .38 NP/.38 S&W or a Police Positive Special chambered in .38 special. No way are they the same.