Red Bear,
I have absolutely no trouble telling the difference between a large bore rifle's mechanical characteristics and those of a shotgun. To see the difference between a shotgun and a rifle, even SxS double rifles and shotguns, simply look at the difference in thickness at various points along the barrel. It is the barrel that contains the pressure. The metallic cartridge is just a gasket to seal the chamber end to contain the gas.
All of the large bore Nitro Express caliber rifles are legal to possess and use in the United Stated although the game appropriate for them is limited. "Sporting use" can be interpreted to mean target shooting as well as hunting. They were all manufactured for sporting use. You are doubting exemptions that already exist. Certainly the law could be changed. The .600 Nitro Express dates back to around 1900 and the .700 dates to 1988.
From page 39 of "The 2014 edition of the Federal Firearms Regulations Reference Guide." (https://www.atf.gov/file/11241/download)
"Shotgun. A weapon designed or re-designed, made or remade, and intend-ed to be fired from the shoulder, and designed or redesigned and made or re-made to use the energy of the explosive in a fixed shotgun shell to fire through a smooth bore either a number of ball shot or a single projectile for each single pull of the trigger."
What makes a shotgun a shotgun is that it is designed to chamber SHOTGUN shells. Brass shotgun shells are not high pressure cartridges. By the BATFE definition "fixed shotgun shell," that is the limiting factor of the difference between shotgun pressures and rifle pressures. The chamber and not the cartridge is the limiting factor in the ability to withstand pressure.