There was another rimmed short .45 revolver cartridge not mentioned, which was one made up specifically for use in the 1907 U. S. Army pistol trials. It was called (unofficially) the .45 S&W Special or the ".45 Model of 1906" (and sometimes the .45 Frankford), but it was never adopted by the U.S. military or sold commercially on the civilian market. Its case length was about 0.92". It is purely in the realm of serious cartridge collectors today as examples are hard to come by. Some were made by Frankford Arsenal, but most were made by UMC, as Frankford had quality problems making it. There is considerable information available about it, some being on this forum. Note that it is not the same as the .45 Schofield or the .45 M1909 (which is simply the full-length .45 Colt case with a larger diameter rim).
Regarding the .45 Colt Government pictures above, I'd bet those are actually .45 Schofield, which is just a shorter cased .45 Colt. The "Government" part comes in as after the adoption of the Schofield revolver, for a long time, the only .45 military revolver cartridge in U.S. service was the .45 Schofield (AKA .45 S&W), which was used in both the Schofield and Colt revolvers. What is their case length? The Schofield (or .45 S&W) had a case length of 1.1".
I have no personal familiarity with the .45 "Cowboy" cartridge, but I understand it has a rimmed .45 Colt case shortened to the length of the .45 ACP case. For use with smokeless powder the shorter case would be somewhat more efficient than the .45 Colt or .45 Schofield cases, both of which were designed for use with Black Powder.