I basically category them in Percussion and Rimfire since those are the main two types that can be haved free. Early, pre 1870, centerfire revolvers can be held free too as
are variations as teat-fire, cup-fire etc. The last two mentioned types belong to a group of interesting guns designed to outsmart the Rollin White patent.
White worked for the "Colt's Patent Firearms Manufacturing Company:" as contract worker. He came up with the idea of drilling the chambers of a percussion revolver cylinder all the way trough. After perfection of his idea he took it to Samual Colt in 1852
but Colt saw no use for it. After Rollin White was no longer needed at Colt he patented it himself in 1855 and signed an agreement with S&W in 1856. As of 1856 only S&W and Rollin White himself could use the idea of loading a revolver from the rear
with catalytic cartridges. Many others copied it but got sued by Rollin White and later S&W. Options were to pay S&W, to produce for S&W or to stop production.
constructions or selling techniques existed to get past the need of loading of cartridges from the rear of the gun. Some special cartridges were designed together with a revolver that could be loaded from the front such as the teat-fire and cup-fire.
Two different approaches I would also like to mention,
both use normal cartridges without interfering with the Rollin White Patent. First the Slocum side loading revolver of which every cylinder chamber slides open to place the cartridge. Second the James Reid Model.4 revolver. That one was sold as percussion revolver but when one screws out the percussion nipples standard .32RF cartridges could be loaded without problems.
When Smith and Wesson introduced their first revolver, Model 1, in 1857 catalytic
cartridges were not new to America. However this was the first commercially available, mass produced revolver to use them, made in the US. The used caliber .22short was not a huge caliber and for usage other than self defense it was not really an option. When
introducing the model 2 in 1863, a larger 6 shot revolver in .32RF long, military use came in sight.
Colt wished to hold on to "Cap&ball" revolvers since he thought shooters would like to keep the choice of the the amount of gunpowder used and so have influence on how the gun
However he was wrong. After his death in 1862 Colt also sought ways to get around the Rollin White patent and when the patent expired in 1869 colt had production models in
centerfire and rimfire calibers ready. In 1873 Colt introduced the famous 1873 SAA (Single Action Army) also known as Peacemaker. That revolver is known to almost everyone since it is almost the only
one seen in Cowboy films letting believe that it was the only one existing. It did however had great impact and is still being made by multiple makers including Colt.