Back when it was the 9x23 CP Elite, a semi-wildcat proprietary round, there were two chamber reamers offered. One was to chamber a new barrel to the optimum dimensions for 9x23. The other was to open up a .38 Super chamber to be sure of accepting the tapered 9x23 case.
And there are numerous .38 Supers that will accept the 9x23 as is. But you need a good stout .38 Super, the chamber pressures are a lot higher.
I don't know about shooting .38 Super in a 9x23 gun. If it chambers freely without "bullet pinch" it will be safe to use; pressures are lower in standard loads.
Most 9x23 owners wanting to buy big and shoot small end up with a spare 9mm P barrel.
Magazines are the same.
Oh, by the way, you might want to look up the difference between semirimmed, rimless, and rebated. I don't know of a rebated rim pistol cartridge since the .41AE and .50AE.