McWood: Williamlayton is correct about the 9x23 Winchester and the 9mm Largo. The Winchester round is a much higher pressure round although it would probably fit the chambers of 9mm Largo/Steyr/Bergmann/Bayard and Bergmann-Bayard, which are all older European 9mm by 23mm length rounds but I dare say the Winchester round would blow a chamber and probably lock the slide back on most of the other caliber pistols. I believe that is why Winchester named the round the 9x23 rather than 9mm something or another, just to avoid that level of confusion and the possibly and probability of a mistake.
You are correct in that the 38 Super, and its predecessor the 38 Automatic, are 9mm (although you can purchase 38 Super barrels with a .357 bore if you want..). You are also correct in that the 9x23 Winchester and the older European 9mm Largo or Long cartridges are simply drawn out or lengthened 9x19 cases. The 9mm cases, all of them as I recall, are tapered slightly whereas the 38 Super and 38 auto are straight walled semi-auto cases with a slight rim, which was the only throw back to the 38 spl revolver round from which they were based, iirc. The 32 acp is also slightly rimmed as you stated.
And your last statement about the 357 Sig and the 357 magnum is also correct. I s'pose Sig could have called it the 9x40 or the 40-9 or the 9/10 or something but they wanted the notion of the 357 magnum capabilities to sell the cartridge and you are correct in that it doesn't hit the 1400'/sec mark, not that you really need it with the 9mm.
And speaking of the 9mm and the 40 in the same handgun - guys, c'mon: the rim dia of the 40 is .424 vs the .391 of the 9mm, and the rim thicknesses vary sufficiently that I believe to shoot the 9mm from a 40mm slide is just asking for trouble with busted extractors, the same way we used to bust extractors by using 9x19mm milspec surplus in the older 9x23mm Largo pistols years ago. Here's what happens when you touch off a 9 in a 40 slide - the barrel centers the round and upon firing pin impact the recoil slams the slide to the rear. The 9mm case is barely held in place by the extractor and the case may 'slap' back and forth or front to rear if the extractor is not tight to the rim, and bust it as it appears there is significant dimentional rim differences in both case rims.
If it were me and I had one Glock or S&W to multi-task with, I would get a 9mm, a separate 10mm slide and barrel combo for field use, a 40 S&W barrel and a 357 Sig barrel to add to the pile - then I think all my 9 and 10mm needs would be met. jmtcw.