Both .357 magnum and the .38 Special can be shot out of a .357 Magnum. The .38 Special was invented well before the .357 Magnum in 1898 while the .357 Magnum was invented in 1935.
This may sound stupid by why didn't they call the .357 Magnum the .38 Magnum instead?
Why was the .38 Special called the .38 Soecial?
When is a .36 not a .36? When is a ..38 a .357?
Let's go back to 1851. The original "Belt Pistol of Navy Caliber" used spherical projectiles of .375 inch diameter--approximately .38.
When patent expirations enabled the use of self-contained cartridges in bored-through cartridges, Colt introduced the .38 Short Colt cartridge. It had an outside-heeled bullet that was larger in diameter than the internal diameter of the case, a la .22 RF, and it fit the old percussion guns.
In 1875, a longer version was introduced for the Colt Lightning, Colt Model P, and other revolvers. It too had a bullet diameter that was close to .38 inches, and it was called the .38 Long Colt.
At some point, the .38 LC was revised to contain bullets of .357 inch diameter. It was still called the .38 Long Colt. It originally had soft lead hollow-base bullets that expanded to fit the larger bore diameter of the early firearms.
The .38 LC was considered underpowered for service use.
In 1898, Smith and Wesson introduced a longer, more powerful version of the .38 Long Colt, and they called it the .38 S&W Special. Why change?
It could be chambered in old .38 LC revolvers that had straight chamber bores. Because firing the new cartridge in those old guns could be very dangerous, later .38 LC guns had stepped-down chamber bores to prevent that.
That possibility became much more serious when new high-powered .38 Special cartridges were introduced. Intended for use in large (".44") frame revolvers, the load was called the ".38-44", and there were warnings all over the box.
The .357 Remington Magnum is essentially a lengthened .38-44 with a higher case capacity and
much higher operating pressures.
It is possible to insert .357 cartridges into an old .38 colt Lightning revolver. Firing them would be disastrous.
That would probably have been more apt to happen had the cartridges were packaged as .38-Something. I would not discount the mitigation of that risk as one reason for calling it a .357-Something rather than a .38.