"Actually a .357 Magnum is a calibre."
No, it's a cartridge designation. The caliber is .357", i.e., 357 thousandths of an inch, which is the diameter of the bullet. The .38 Special cartridge uses the same diameter bullet, as do various other cartridges.
"It's like saying a 9mm Luther (a very popular 9mm round)."
There's no such thing as a "9mm Luther." There is however, a 9mm Luger (AKA: 9mm Parabellum, AKA: 9×19mm NATO), which, like ".357 Magnum" is a cartridge designation. The caliber is 9mm, or .355" in U.S. customary units. There are a lot of other cartridges that use the same caliber bullet, such as the .357 SIG, .380 ACP, etc.
"Magnum makes ammunition as well as guns"
"Magnum" doesn't make anything, as it's not the name of a company. It's a generic term that originally referred to an extra large bottle of wine and was later used by various gun companies to indicate a larger / more powerful cartridge. The full name of the cartridge is .357 S&W Magnum; Smith & Wesson was the company that developed and introduced it to the commercial market.
"much like how Smith & Wessson make the S&W .40 cal and you get all sorts of guns that are chambered in that"
Smith & Wesson isn't an ammunition manufacturer. It is called ".40 S&W" because Smith & Wesson is the company that developed and introduced it, and that's what they decided to name it. And again, that's the name of the cartridge. The caliber is .40", or 10mm in metric units.