The number on the butt (C 113120) is "the" serial number. The number stamped on the frame behind the yoke (18487) is an assembly number, unrelated to the serial number. Smith & Wesson did this because the yoke (the part the cylinder swings out on) and frame were fitted together before the frame was serial numbered, and it was necessary to insure these pre-fited parts got back together later.
Besides the butt and cylinder rear face, the serial number is also stamped on the bottom of the barrel (above the ejector rod), inside the sideplate, and the inside of one stock panel - if the stocks are original to the gun.
Mass confusion has occured now because later the company moved the serial number to where the assembly number used to be behind the yoke. The reason was that they were more likely to fit revolvers with stocks that covered the butt.