I have just completed a review of the origins of the early .44s. My conclusion is that the 44 S&W American and the 44 Henry center fire are both independantly conceived cf versions of the 44 Henry rf.
The 44 Colt seem to come to a similar solution, but via a different route. The 44 Colt and its twin, the 44 Remington, are Frankford Arsenal developements whereby a new cartridge, centerfire being preferred from the beginning, was designed to fit into an existing 44 Cap and Ball cylinder with the absolute minimum of re-working. The dimensions are remarkably similar to the 44 Henry. In front of me is an article in The Shootist, March/April 2000, by Bob Edwards, page 36. He noted the similarity to a 44 Henry rf in his collection. Others have made the same observation.
Soo Close! But, different.
Now, take the lineage to the next step. 44 Henry rf is altered to the center fire 44 S&W American at the behest of the Ordnance Board in 1870. Shortly thereafter, the Russians want boatloads of revolvers, but want them with an inside lubricated bullet. The simplest solution is to ream out the cylinder just a bit for a slightly larger case that can accomodate the same bullet diameter inside the neck. Now we have the 44 Russian. Later, when smokeless powder became popular, in the 20th Century, the case was lengthened, as the 44 Special, to prevent the new, higher pressure ammunition from being chambered in older cylinders. Finally, Elmer Keith inspires the .44 Rem. Magnum! The last three are a family, one taller than the next, and a shorter one can fit a longer chamber.
Every story has a wild card. In this case there is the "MODERN" 44 Colt. While the original had a itsi-bitsi rim and a heeled bullet, the modern version uses slightly altered .44 Russian / Special cases and a .429 barrel to take advantage of standard modern .44 bullets in .429.
Got that?