Carmady is correct. The reason the company originally gave for not using the .22 LR was that the combination of a light crimp, a heavy bullet, and a light gun caused the bullet to jump forward on recoil and tie up the gun. Nothing was mentioned about pressure (and SAAMI spec for the .22 Long and LR is the same, 24,000 psi), but I have seen one Ladysmith with a cracked cylinder and several sources mention bulged barrels. I would avoid using .22 Long and using lightly loaded shorts. Or maybe better yet, not firing those guns at all.
(Of course today's .22 LR rounds are heavily crimped but in those days, the cartridge was shot only in heavy target rifles and it was thought that a heavy crimp spoiled accuracy.)
As far as I can find out, the term ".22 S&W" was simply marketing. While some ammunition companies sold it, I cannot find how, or if, it differed in any way from regular .22 Long.
Jim