Paper cartridges were commonly used for muskets and rifles in the CW era; .58 cartridges were made with paper that was emptied and discarded. (For the obsolescent .69, the paper was stuffed into the barrel with the bullet.)
But for revolvers, there were several kinds of cartridges. Those made at the government arsenals were usually of the same kind as those for the rifle, that it is they were encased in paper with the normal "tail"; the paper was discarded after the powder and bullet were loaded into the cylinder.
Those made by contractors varied, and there was even one in which the powder, soaked in collodion, was simply molded on the rear of the bullet, making a convenient and waterproof cartridge. It might have become more popular had the factory not blown up.
Colt's commonly used nitrated paper, but other common ways to contain the powder were skin (not unlike a sausage) and foil. All of these broke under the pressure of the rammer and were burned up or blown out of the barrel when the chamber fired. (The foil, incidentally, was true tin foil, not the aluminum foil common today.)
For military issue, revolver cartridges were usually packed in wood blocks holding six cartridges, along with 6 (or 7) percussion caps. The blocks were then wrapped in paper which was varnished or waxed, thus making the packet waterproof until opened. Unlike rifle cartridges that were often destroyed by moisture or by jostling in the cartridge box, pistol cartridges were fairly well protected and many packets have survived intact.
Jim