It is the .41 Rem Mag if you want to be fully correct.
The rivalry between gun makers goes waaay back, and sometimes cost them more than they expected. The classic rivalries are Remington vs. Winchester (rifles, primarily but shotguns too..) and Colt vs. S&W.
Looking back at the history, we see that, for a LONG time, Remington would not chamber their rifles in Winchester cartridges, and Winchester would not chamber theirs for Remington's.
And Colt wouldn't make a pistol for a S&W cartridge, sort of. Anything with the S&W name would not be put in a Colt gun, as Colt didn't want "S&W" being marked on their guns.
SO, what they did, rather than take the route Winchester and Remington were on (competing cartridges that were essentially the same performance niche, but different cases), what Colt did was to make "Colt" cartridges, dimensionally the same as the S&W ones, but loaded with a different style of bullet (usually a flat point of some variety). And putting "Colt" in the name of "their" cartridge.
Look at the pre-.38Special .38s & .32s and you see this several times. Not every one, but several. Eventually Colt stopped bothering with their own "cartridge" (which was actually only a specific loading), and simply dropped the "S&W" from the cartridge name marked on a Colt gun.
This is, essentially, how the .38 S&W Special became the "simple" .38 Special.
(don't confuse the .38 S&W Special with the .38 S&W, they are different cartridge cases)
Colt made a few rifles in the early days of cartridges (which weren't hugely popular), then, according to gun legend, entered into a "gentleman's agreement" with Winchester. Colt would stay out of the rifle business, if S&W stayed out of the handgun business.
Real or not, this became the tradition, and it lasted for a very long time.
I had heard the story about how Ruger "found out" about the .44 Mag, just didn't include it as it came after the cartridge was already in development. The interesting thing is that while S&W was "first", in the early years Ruger actually got more of their .44 Mags into the general market than S&W did.
Strange as it may seem today, in the early years, the .44 Magnum was not a popular round, and comparatively few were sold. After 1971, that changed radically. Sales skyrocketed, thanks to Dirty Harry, and the .44 Mag has been a popular seller ever since.
If you think today's price bubble on guns is bad, take a look at the early through mid 1970s. S&W was running two years behind in delivery of .44 Mags, and people were paying as much as 2X retail price for a S&W M 29. A good friend of mine paid over $400 for a nickel 6" when the MSRP was $283.50! (and he was earning about $300 a month at the time!) But he got one.
There were a lot of .44 mags on the used market as supply caught up with demand. Lots of times one would see a .44 Magnum (either S&W or Ruger) in the used case, with a box of ammo containing 44 rounds......