S&W manufactured three versions of the .32 Safety Hammerless 1888-1937, several other firms foreign and domestic more-or-less copied them.
.32 S&W is shorter than .32 S&W Long. The .32 S&W can be fired in the Long. Pesuming it is truly a Smith, give me a serial number, if redacted use X's for the last few numbers and I can tell you which version and the range of manufacture.
The third model ran from 1909-1937, serials 170,000 to 242,981.