The old S&W .32-20s are interesting guns. The serial number on yours suggests manufacture around 1920/21. Does it say .32-20 on the barrel? Or .32 WCF or .32 Winchester? Those are all the same cartridge.
If it says .32 Long, that's a different cartridge and I want to buy the gun.
The lanyard loop is a little surprising; its presence makes me think of police or military use. I'm not sure civilian models came with the loops, though I imagine you could get any feature you wanted on a special order. The four inch barrel also speaks to
Those stocks may not be slightly older than the gun they are mounted on. The gold medallions are usually seen on 'teens-era revolvers. During the '20s, S&W stocks had no medallions. In the '30s, medallions came back but were silver in color.
In case the Antiques moderator looks at this thread, maybe it could be moved over into the 1896-1961 section. Despite its age, this gun is really one of the "modern" hand ejector models.
EDITED TO ADD: On closer inspection, something seems not right to me about the trigger guard profile. Do you see the words "Smith & Wesson" or the S&W logo anywhere on the gun? Maybe I am too suspicious, but I wonder if this could be a S&W knockoff.
EDITED AGAIN A FEW MINUTES LATER: I'm pretty sure this is not an authentic S&W. For its presumed age, it should have an exposed hammer stud and rebound slide pin on the left side of the frame. Neither is visible on your gun.