I'm pretty sure the difference is not shot size but the powder burn and speed of shot fired, HP shot was developed to hit game with more energy at longer distances as steel shot does not have the same energy as the same size pellet in lead, a gun that is HP proofed at full choke for those distance requirements or clay shooters who use tight chokes like trap shooters will need to have a gun capable of this requirement.
All guns, it has been reported can use nitro steel shot upto 1/2 choke, although it is my understanding that even with half choke the size of the shot size must be a consideration. It's to do with the lack of deformation of steel shot going through the choke constriction.
It is also my understanding that most guns proofed for HP at full choke are fixed choke guns. A few screw in choke/gun manufacturing companies have chokes that can take steel at full choke, fabarm guns and Muller chokes are two that I'm aware of. I am not sure if Fabarm can take HP steel at full choke with their screw in choke.