S&W started a completely different type of frame nomenclature when the brought out the Hand Ejectors in the 1890s.
Because there was a considerable overlap in production of the breaktops and the Hand Ejectors (about 25 years), there needed to be an easily understandable way of differentiating between them.
Since the breaktop frame sizes were numbered, letters were the logical way to go.
Most people didn't even know about the lettering system for frames until AFTER World War II, when S&W went from model names to model numbers for the Hand Ejectors.
The old breaktops, however, were readily identifiable, as the model name and frame number were often used in company literature, i.e. S&W American No. 3, which was the large frame (No. 3), single action chambered for the .44 S&W cartridge. After the development of the .44 Russian cartridge, which was a lengthened version of the .44 S&W, that cartridge came to be known as the .44 American. From those two cartridges came the .44 Special in 1907 and the .44 Magnum in the 1950s.
Hardball, if you do want to shoot your LadySmith, do NOT use modern ammo! These guns will simply not take a diet of modern .22 Long or Long Rifle ammo.
Your best bet is to try to find, probably from Old Western Scrounger or Dixie, some of the ammo that has been made specifically for use in these older guns.
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Beware the man with the S&W .357 Mag.
Chances are he knows how to use it.