Thanks for giving the correct dates. My memory sometimes seems to be not as reliable as it once was of late.
As I've read it, until the Rollin White patent on bored-through cylinders held by S&W had expired NOBODY could produce a metallic cartridge revolver using that feature without paying S&W for the rights, and they weren't selling.
Their .44 cal. No.3 revolver was the first truly practical cartridge big bore produced and it had that market to itself for at least a couple of years. When the patent did expire, Colt began making the Richards 1860 Army conversions first in .44 Henry Flat RF, and then in .44 Colt. These were followed by the 1872 "Open Top" model.
At first, a relatively small number of the Colt conversions in .44 Henry were acquired and tested by the Army. They liked the revolver well enough, but not the cartridge. They also purchased and tested the S&W No.3, with much the same conclusion.
When the Army outlined the requirements for a new service revolver contract, they specified that it must use a centerfire cartridge with a bullet of at least 0.45" dia.
In order to submit their No.3 for the contract tests, S&W designed a new .45 cartridge that would fit into their existing revolver, as did Colt in the 1872 model they were to submit. The Army liked Colt's cartridge best, but found both of the revolvers' designs to be lacking in some respects. Colt went to a top-strap design and resubmitted. It won the contract and was adopted as the Model of 1873.
It wasn't any patent that kept S&W from chambering their revolvers for the Colt cartridge: The revolver simply could not be made to accept it without a major redesign, which would've also entailed the complete revamping of their manufacturing operations.
Cavalry officer Major George Schofield liked most of the S&W design, but (on his own, not in direct conjunction with S&W) redesigned and patented an "improved" latching system to allow for one-handed manipulation by a mounted cavalryman. As he had a brother who, I believe, was a Honcho on the Ordnance Board it came to pass that the S&W No.3 using the Schofield latch became approved for issue as a Secondary Standard.
For the use of his patent, S&W agreed to pay Maj. Schofield a whopping $0.50 per revolver sold, which netted him perhaps $3,000 all told. Ironically, he died, broke and bitter, by one of them in his own hand.