Howdy
Blue is not like paint, it does not have any thickness. If a firearm is badly rusted and pitted, it will usually be polished down to remove the rust and pits. Then it is reblued.
What you have there is a Registered Magnum that has sadly been overpolished by a refinisher who did not know what he was doing. The Registered Magnum program was a marketing campaign started by S&W to introduce the 357 Magnum cartridge in 1935. Each Registered Magnum had a registration number stamped on it, and the owner received a registration certificate from S&W. The Registered Magnums were custom guns, produced to the specifications of the person who ordered it. There were 23 barrel lengths to choose from, six types of sights, service grips or Magna grips, and the gun could be finished blue, nickel plated, or it could be engraved. As previously stated, the Registration number for this one is 3986.
S&W never intended the Registered Magnums to be a high volume product, the factory could only turn out about 120 of them per month. The catalog price for a Registered Magnum in 1935 was $60, $15 more than any other revolver in the catalog. That was a great deal of money in 1935, at the height of the Great Depression. Even so, demand for the Registered Magnums far outstripped the ability of S&W to supply them, so in 1939 S&W did away with the Registered Magnum program. About 5,244 Registered Magnums had been produced, Serial Numbers ranged from 45768 to 62489. After 1939, The 357 Magnum continued to be produced, but the choice of options was greatly reduced. In 1957 S&W changed over to a numbering system for all their firearms and The 357 Magnum became the Model 27.
You can see how this one was overpolished by the refinisher. The lettering of the markings is over polished and no longer as crisp as it was when first produced. Compare how blurry the markings on the surface of the revolver are to how crisp the markings down under the cylinder yoke are. You can also see some of the screw holes have been slightly dished, and the joint around the side plate has been rounded over. The joint should be almost invisible. You can also see how the trademark markings on the rear of the hammer have been blurred. The serial number on the bottom of the butt of this revolver appears to match the serial numbers on the rear face of the cylinder and the inside of the relief under the barrel for the exactor rod. The serial number should also be stamped on the underside of the extractor star. This will indicate that those parts are original and the revolver left the factory with those parts.
Regarding the logo, many S&W revolvers of that period had a small S&W logo deeply stamped on the left side of the frame. Overpolishing would probably not have removed it. At some point, a larger logo was stamped on the side plate. This logo was not so deeply engraved and it is possible the refinisher completely obliterated it when he over polished the side plate.