Not quite correct.
The name of that brass is 45 Cowboy Special. Same rim design as a 45 Colt, same length and internal capacity as a 45ACP.
A 45 Cowboy Special round is in the center of this photograph. Left to right the cartridges in this photo are 45 Colt, 45 Schofield, 45 Cowboy Special, 45 Auto Rim, and 45 ACP. 45 Cowboy Special was developed specifically for light Smokeless powder loads, often used in Cowboy Action. Typical 'mousfart' 45 Colt loads, which may have very light powder charges often exhibit inconsistent ignition and performance because of the large internal capacity of the 45 Colt case. Putting the same charge in a case the length of a 45ACP can improve ignition because of less airspace in the cartridge. The 45 Colt style rim allows the round to be chambered in any revolver that will chamber a 45 Colt. Putting Black Powder into a 45 Cowboy Special also results in a milder charge than a 45 Colt with 35 or so grains of Black Powder.
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A comment I will make: Lots of folks talk about XX.X grains of Black Powder. Not all Black Powder weighs the same. Many years ago I made up this chart with the actual weights of some of the common Black Powder charges that I use in several cartridges. As a standard 'volume measurement' I have referred to the various Lee Dipper sizes I have used in the past. They are calibrated in Cubic Centimeters, which are the same as Milliliters. Sorry, only five brands and granulations of powder are in my chart as that is what I was using at the time.
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One more comment: The original "40 grain" government 45 Colt cartridge was the copper cased, Benet primed version as produced by the Frankford Arsenal in 1873. These cases had more internal capacity than the later balloon head cases, and also more than modern solid head brass. This is a photo of a copper cased, Benet primed 45 Colt and 45 Schofield cartridges. The large crimp near the bottom held an Anvil Plate against the bottom of the case. The priming material was deposited on the inside of the bottom of the case and the Anvil Plate pressed onto the priming material. When a firing pin struck the rear of the soft copper case the copper compressed the priming material against the Anvil Plate, igniting the priming material. The flame generated passed through two flash holes to ignite the Black Powder charge. From the rear, these cases look like rimfire cartridges, but they are not, they are an early form of centerfire cartridge. This style of cartridge had more internal capacity than either balloon head cases or modern solid head cases.
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A box of twenty rounds of copper cased, Benet primed rounds from the Frankford Arsenal. This box was produced in 1874 and has the reduced charge of 30 grains. One of my 45 Colt reloads in a modern solid head case on the right for comparison.
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In this photo a Remington balloon head 45 Colt case is on the left, a modern Winchester solid head 45 Colt case on the right. I sawed both cases in half as a visual indicator of how much more internal capacity the old balloon head style cases had than modern solid head cases.
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Not saying one cannot stuff 40 grains into a modern case, but it will have to be compressed considerably more than was necessary with either the old copper cases or the balloon head cases.