Pilgrim,
The stuff that looks like a .22 short is a modern cartridge that we call the .22 BB cap. The original Flobert was a tapered cartridge without a distinct rim, formed from a musket cap and loaded with a 15gr. round ball, like the picture. The cartridge goes back to the early 1840's and was the basis for the .22 rimfire. The name "Flobert" is now used generically to refer to these type of short cartridges that have a combined priming and propellant.
The Flobert cartridges and guns are still fairly common in europe, in calibers from .22 (6mm) to 9mm. A Google search for "Flobert cartridge" will turn up some photos of these cartridges for comparison.