Remington
He is shooting a Remington black powder revolver converted to fire cartridges.
I think Uberti used to sell a version of it.
The loading lever on the cap and ball 1858 Remingtons served to force the bullet into the cylinder and to hold the cylinder pin in place.
After the Smith & Wesson patent on bored through cylinders expired, other manufacturers started converting their products to fire metallic cartridges. Due to the design of the gun, the loading lever on the Remingtons was retained for a few years after the guns were being manufactured specifically for cartridges to hold the cylinder pin in place while the gun was fired. It was dropped in later models.
In Pale Rider, Clint carried several extra cylinders in pockets on his belt.
When he needed to reload, he lowered the rammer handle, pulled out the cylinder pin, dropped the expended cylinder out, inserted a loaded cylinder, reinserted the cylinder pin, and locked the rammer handle back in position.
This form of "speedloader" was used by many paople who carried cap and ball revolvers both before and during the War of Northern Aggression. This reloading process is not the safest thing to do because it is easy to knock a percussion cap against the frame and cause the chamber to fire. The same risks apply to metallic cartridges today.
This practice is STRONGLY DISCOURAGED.
