Hi Hewy, you are correct, the Pietta 1862 is more like an 1861 Colt, not 1862. The Uberti 1862 is very faithful to the original design. I have both and frankly favor the Pietta 1862 over the Uberti for a few reasons. The Uberti is 5-shot, the Pietta 6. The Uberti is a terrible cap sucker, the Pietta like an 1851, not too bad. The Howell (Taylor) 1851 conversion cylinder (38 Colt/38 Special) will work in the Pietta, the only conversion cylinder for the Uberti 1862 is a .22. The Pietta 1862 fits the hand better than the Uberti and can use Pietta 1851 extra cylinders and parts.
IMO the Uberti 1862 is one of those last revolvers on a BP revolver wish list to acquire, kind of like the Paterson and LeMat.