Daryl:
Quite so: the short was the original .22 rimfire cartridge, however I suspect that for the last couple of decades of the 1800s most break-open single-shots were chambered long to accept both the short and the long cartridge. Later repeaters were commonly chambered for the .22 Short specifically, probably for greater mag capacity in the popular tube magazines at the time.

Unfortunately the .22 Short is no longer the cheap practice round it once was!