It does get a bit confusing...
Between 1908 and 1942, the Police Positive was chambered to use the following cartridges.
.22 RF (short, long or long rifle)
.22 WRF (Winchester Rim Fire - a unique .22 round)
.32 Colt New Police (same as .32 S&W Long)
.38 Colt New Police (same as .38 S&W)
At the same time the Police Positive Special was chambered in:
.32-20 WCF (originally designed to be used in Winchester lever action rifles & carbines)
.38 Special (also would fire .38 Long Colt, but not .38 S&W)
Following World War Two the Police Positive was discontinued, but the Police Positive Special remained in production. At that time the .32-20 option was dropped, but for a short time the .32 S&W Long and .38 S&W chamberings were added. Some were also made in .22 Rim Fire.
Clear as mud?