Howdy
Smith and Wesson adopted their present nomenclature of using model numbers in 1957. At that time S&W began stamping the model number on the frame under the cylinder crane. Swing out the cylinder and look under the crane. If the gun was made after 1956 it will tell you what model it is. This particular gun is a Model 28. The letters 'MOD' will always be present. Then there will be a two or three digit number indicating the Model Number. This may or may not be accompanied by a dash and another number. The dash indicates which engineering change the gun represents. But if it was made after 1956 there will always be MOD XX or MOD XXX stamped on the frame under the cylinder crane. The numbers above the MOD 28-2 on this gun are assembly numbers and have nothing to do with the model number.
If there is no model number under the cylinder crane then it is a pre-1957 gun, and the 357 Magnum models made before 1957 are pretty limited limited in scope.
Almost all the 357 Magnum revolvers made by S&W before 1957 were built on the large, or 'N' frame. This limits them to The 357 Magnum, which was the model name of the original 357 Magnum revolver, also known as the Pre-Model 27, and the Highway Patrolman, sometimes known as the Highway Patrol, also known as the Pre-Model 28. The Registered Magnums were a marketing trick used by S&W for the first 5200 or so 357 Magnums. If you have stumbled onto one of these, grab it and run, but I kind of doubt that you would find one at a yard sale. Basically, if it is a large frame pre-model number revolver chambered for 357 Magnum, the only two models were the 357 Magnum and the Highway Patrolman. The 357 Magnum, and its successor the Model 27 were highly polished, and had checkering on the top strap and along the barrel rib. Like the revolver on the left in this photo.
The Highway Patrolman and its successor the Model 28 had a more utilitarian finish. The blue was not as highly polished, and there was no checkering on top.
The only other possibility if it is a pre-1957 357 Magnum revolver is The 357 Combat Magnum. This revolver was introduced in 1955 and was built on the medium sized 'K' frame. In 1957 the 357 Combat Magnum was renamed the Model 19.
Here is a photo that compares large frame (N) Model 27 to a medium frame (K) Model 19. Do not be confused by the size of the grips, the larger framed Model 27 at top is a bigger gun than the K frame Model 19 at the bottom of the photo.
This photo illustrates the difference between a large frame (N) 357 Magnum and a medium frame (K) 357 Magnum. The large frame accomodates a much larger cylinder, which has a lot more steel surrounding each chamber than the smaller gun.
That's pretty much it. Look for a model number under the cylinder crane. If no model number, determine what frame size it is. If there is checkering on top it is The 357 Magnum. No checkering it is a Highway Patrolman, or the smaller Combat Magnum.
P.S.: A Highway Patrolman will say so right on the side of the barrel.