They have chambered pistols in 460 Weatherby.
I have had a Contender pistol in 357 Herrett for many years. It is a shortened and blown out 30-30.
I now have its bigger brother, the 358 Yeti, chambered for the AR-15. It is a shortened and blown out .308.
I also had a 256 Ferrett Carbine. It used a 357 Magnum case necked down to 25 Cal and shot out of a modified M1 Carbine. Also known as the 256 Win Mag.
I'm guessing that orthopedic surgeons love a .460 Weatherby pistol - great for business. That pistol seems to be another example of just because you can do it doesn't mean that you should.
To answer your first question, I would say a caliber that is first popularized in a pistol and then migrates to a rifle.
A .41 magnum in a Ruger Blackhawk pistol and a companion Henry Big Boy carbine are on my wish list.
I would say what they were originally developed for.
If they were developed for a hand gun or developed for a rifle.
My 14 inch 45-70 contender barrel does not make the 45-70 a pistol cartridge.
My 357 mag in my marling carbine does not make the 357 mag a rifle cartridge.
Putting rifle cartridges into bolt action hand rifles do not make them pistol cartridges.
Yes things a little grayer now but duel caliber pistol/rifle/carbines cartridges have been around for along time.