Van Pelt's weapon was strictly fictional. Special effects people dressed up a M1901 Winchester shotgun to get the look they wanted. It's cartridge was fictional as well.
As to your other question, Cartridges get discontinued all the time.
Robert E. Walker writes in Cartridges and Firearm Identification,

There are many hundreds, if not thousands, of different cartridges, the majority now being obsolete or passing into obsolescence. More cartridges are extinct today than are commonly encountered, having passed into history with improvements in technology, either in some element of the ammunition or the guns that used them.

Cartridges that were old standbys when I was a young man, like the .250 Savage, or were the new wave of the future, like the 8mm Remington Magnum, have fallen by the wayside.
Around 1900, a lot of them would have been falling out of use.
The firearm cartridge, as we know it, was really a product of the 1860s.
Early cartridges were designed around black powder. But by the late 1880s the development of more powerful smokeless propellants was changing the technology of firearms. A lot of those old black powder cartridges would become obsolete, and get discontinued when the market for them got small enough.