The 56-52 was actually developed prior to the 56-50. It is loaded with a heel base bullet, and outside lubed, diam. a nominal .520 +/-. The 56-50 has an inside lubed bullet, and a diameter in the original of .515 +/-. It was developed by Springfield Armory and was done to provide a more efficient load. The case is longer and allows for the same powder charge with the same overall length allowed in the Spencer action, even a heavier bullet. The 56-52 can be fired in the Original 56-50, as the bullet is swaged down in the bore, but the 56-50 cannot be fired in the 56-52 without loss of accuracy due to the smaller bullet.
The calibers on the Spencers are a bit misleading, as the Spencer utilized barrels from Sharps initially, and the caliber varied with the supplier. Most were a nominal .54 caliber, and a majority of the ones produced at later dates had a .52 caliber bore. The ammunition was supplied slightly oversize to allow for use in any of the barrels. Firepower, not target accuracy was the objective. Also remember that ammunition manufacturing was in its infancy.