Howdy
The first one, with the four inch barrel and curved butt with hard rubber grips is interesting. Yes, it is a 32-20 Hand Ejector, Model of 1905. Does the Serial Number you show on the inside of the grips also appear on the bottom of the butt? If so, that is a 32-20 Hand Ejector, 2nd Change. The range of Serial Numbers for that model runs from 33501 through 45200. These were made from 1906 until 1909, when the 3rd Change kicked in with some internal changes.
Caution: That revolver probably does not have a hammer block inside. If it does, it is an old, obsolete version of the hammer block. In extreme situations, if dropped on the hammer with a loaded round under the hammer, this model could discharge.
I'm not sure when S&W stopped making the 38 Military and Police with a round grip. This 38 Military and Police left the factory in 1939. Now notice how different the shape of the knob on the front of your ejector rod is from the front of the ejector rod on this one. The mushroom shaped cap says your 32-20 is much older than this example, it would be consistent with a S&W revolver made in that earlier time period.
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The larger revolver is easier to pin down. Officially, that model was known as the K-38 Masterpiece, although some call it a 'pre-model 14'.
First produced in 1948, this was the first 38 Special revolver that S&W produced with the modern 'click adjustable' rear sight. Earlier target 38s had two tiny screws to adjust for windage, the new rear sight used one large screw on the right side of the sight. This one shipped in 1950. In 1957, when S&W went to a model numbering system, the K-38 Masterpiece became the Model 14.
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The Serial Number on the butt of your K-38 Masterpiece indicates it shipped in 1948, the first year of production. This model should be completely safe to load with six rounds, it should have the modern style hammer block inside that S&W has put inside every revolver since 1944. Unless some idiot removed the hammer block. Notice the shape of the hammer. This was called the Speed Hammer and it was an early version of the 'short throw ' hammer. The front sight is known as a Patridge front sight, designed for target shooting, not so great for drawing from a holster because it can drag bits of leather with it.
The caliber marking on S&W revolvers of this era used what was known as the Lazy Ampersand.
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Note too, your K-38 has the early style tapered barrel with a narrow rib. Later versions of the K-38 had a barrel the same diameter its whole length and had a wider rib.
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Your K-38 Masterpiece appears to be in excellent condition. You will notice there is a little bit of muzzle wear on mine.