The .416 Taylor is a necked down .458 Winchester. Just run .458 Win brass through a .416 Taylor full length sizing die and one has a .416 Taylor case, minus the correct headstamp for the cartridge.
The .416 Ruger was a good idea of a cartridge for standard length (.30-06 size) actions, without the belt. The case is from the .375 Ruger which to my limited knowledge is not formed from an older cartridge. Who cares? Anyone trying to find brass for loading their own ammo, or trying to find factory loaded ammo other than what is available from Hornady. Another decade and the Ruger cartridges may be like the Dakota proprietary cartridges, gone the way of the dodo bird.
Note: The .458 Win was designed for a standard length action for the same reason that drug dealers give future junkies the first hit of crack for free. Once hooked, they will come back and back and back for more crack or in our world, ammunition. Winchester could not have been sellign .458 Win ammo to thousands of converted Mauser owners if the new cartridge would have been released in .375 H&H length.
The .416 Taylor has less case capacity than either the .416 Rem or Rigby but it has enough to drive a 400 grain bullet to 2350 fps. A careful handloader could push the Rem or Rigby cartridges to 2450 fps but why bother? The originally .416 Rigby load was for a 410 grain bullet at an advertised 2350 fps. The actual velocity may have been somewhat less than that. There were NOT many tools for measuring velocity available to consumers or handloaders a hundred years ago. FYI, when I shoot factory ammunition across my trusty Lab Radar I find that advertised velocity isn’t always so. A difference of 20 or 30 fps could be attributed to variances in the chamber dimensions of a test barrel and whatever barrel I am shooting. But 50 fps or more is suspect!
My opinion as an experienced shooter and ballistician rather than a 20-time African hunter is that the .416 caliber cartridges provides the middle ground in power and range compared to the trusty, do anything .375 H&H-class and the .458 and larger class dangerous game cartridges. Someone who has shot everything on the planet including a blue whale with a .375 may dispute that. Or one who specializes in elephants may very much prefer a .500 or larger rifle. But, I think the .416 class is in the middle...
Of the available .416 dangerous game cartridges, the Rigby has the most nostalgia but requires a magnum length slightly larger diameter action, the Remington with today’s temperature stable powders is the most practical but requires a magnum length action, the Ruger is a great design for standard length actions that was introduced far, far to late, and the Taylor should have been introduced as a factory cartridge long ago. But, it is far too late for that.
The cartridge that Remington introduced was very similar to the wildcat .416 Hoffman. Big Green wasn’t in business to give anyone else credit for their good idea. Hmmm, this reminds me of the .416 Ruger being released rather than chambering rifles for the old timer .416 Taylor.