I have a 3" Ruger SP-101 in .327 Federal so I do know about the different .32s it can shoot.10mm Auto - introduced 1983. Derived from the .30 Remington case. Case length 25mm.
During FBI testing in 1988 a reduced-power load was developed to reduce felt recoil to the level most FBI agents found acceptable. Only usable in large-framed pistols and revolvers.
.40 S&W - introduced 1990 as a shorter-cased (22mm) substitute for the "10mm FBI" load, so as to be usable in more pistol designs - specifically the medium-frame pistols currently firing 9mm.
The bullets are identical, and interchangeable (for example, Hornady specifically labels its offerings with '10mm/.400" '.
Neither is to be confused with the 10mm Magnum (31.9mm case length). Introduced in 1992 in the Automag IV. Basically a lengthened 10mm Auto. Uses the same bullets as the .40 S&W and 10mm Auto.
A number of revolvers are set up to fire all 3 cartridges from the same cylinder, moon clips required.
So one could say that those cartridges are the .400" rimless semi-auto version of the .32 S&W Long / .32 H&R Magnum / .327 Federal Magnum!
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