The .40 is that in between caliber that some skip over. One story is that S&W came up with it as an alternative to the 10mm that the FBI found had too much recoil for it agents.
That is not a "story." In actual fact, the FBI came up with its recipe for the 10 mm Auto, which it found would do everything they wanted in their multi-barrier ballistic gelatin tests. The FBI recipe for its service round reduced the 10 mm from 200 grains at 1,200 foot seconds to 180, and then 190, grains at roughly 995 fps.
The FBI 10 mm ammo as issued to agents allowed the use of its standard service round (190 gr. at 995 fps) or a "Magnum" version, the full power 10 mm which was 200 gr. at 1,200 fps. This was similar to its long-standing practice of using a service round, but having available a more powerful round for special circumstances. This is most easily illustrated by the FBI +P 38 Special standard service load in the .357 Magnum guns, into which Magnum ammo could be used upon special permission.
Tommy Campbell, then with S&W and perhaps others thought that a 10 mm cartridge casing could be shortened to allow it to function in a "9mm length action," and still duplicate the ballistics of the FBI Service round.
S&W and Winchester worked together and introduced the Model 4006 (developed by S&W) and the Winchester .40 S&W ammo (jointly developed), which was 180 grains at 990 foot seconds, roughly, and the rest is history.
Those not impressed with the ballistics of the "castrated" 10 mm cartridge disparagingly referred to the .40 S&W as the ".40 Short and Weak," the "10mm Short," or "10mm Lite." The round was so new that the California Highway Patrol, at the time it adopted the S&W 4006 and the new .40 S&W round refers to the round as the "10 mm Short" in the report. Glock submitted an experimental version of what became the Model 22 to CHP, but the report, which I have read, details numerous failures of the pistol. In fairness to Glock, if I recall, they claimed at the time that the pistol submitted was an experimental model and they did not expect it to be subjected to the grueling tests.