The .44-40 is really an impressive round. It's not surprising that frontiersmen took to it as the standard round for both revolvers and lever action rifles.
A 200gr bullet at 1245 fps is not far from .44 mag territory.
I love shooting the .44 special. I probably shoot 10 .44 specials for every .44 mag.
.44 Special and the famous Charter Arms Bulldog. 
The .44-40 was a Winchester development, also called the .44 WCF for Winchester Centerfire, an improvement over the .44 Henry. It is a slightly bottlenecked case, which improved it’s feeding in the 1873 rifle and was introduced the same year.
“The .44-40 is the cartridge that replaced the .44 Russian. The .44 Special didn’t come around until 1907. ...”
The 44-40 (first known as 44 Winchester Centerfire or WCF) was introduced in 1873; the 44 Russian was introduced in 1871. Both enjoyed very long service lives, commonly available until WWII. They satisfied different requirements: the 44-40 was a rifle cartridge, the 44 Russian a revolver cartridge.
Early 44-40 loads matched performance of handgun rounds like 45 Colt and lent no special advantage to a revolver shooter. With the advent of nitro propellants for commercial ammunition in the 1890s, Winchester developed high velocity loads for the 44-40, but these were safe only in rifles.
With commercial competition being what it was in the later half of the 19th century, manufacturers did not standardize chamber dimensions well. 44-40 suffered a loss of reputation for accuracy, especially from handguns, whose makers did not always duplicate Winchester’s chambers adequately; furthermore, headspace had to be generous to permit function. And 44-40 was (and is) a fussy handloading proposition, with very thin case walls and gentle taper. In contrast, the 44 Russian, squat and straight-walled, was blessed with a strong cartridge case and reloaded easily.
44 Russian enjoyed early success as a target cartridge and dominated long-range events for some years. So great was its reputation that Colt’s was still marking its New Service revolver “44 RUSSIAN and SPL” in the 1930s.
The 44 Special had a longer cartridge case; writers have postulated that this was to make room for early bulky smokeless powder, but factory ballistics duplicated the Russian. The 44 Magnum (1955) was built longer still, specifically to prevent its chambering in earlier, weaker guns.