I think that what your are referring to is possibly the "conversions" such as the Richards & Mason - which was a conversion of the standard 1851 Colt Navy. You then have the 1871/72 "open top".
The 1851 Richards & Mason were originally converted to cartridge - the 38 Colt Short (parent of the 38 Colt Long which was parent of the 38 Sspecial) was developed for these conversions. The 38 Colt Short would have been ballistically very similar to the modern 380 ACP cartridge. Because their bores were first bored to .360l and then rifled, the cartridge required a "heeled bullet" in order to grip the rifling on the way out.
The 1871/72 Colt "open top" was designed as a "cartridge gun" - utilizing some 51 Navy parts Colt still had in stock. The revolver was chambered in 44 Henry Rimfire - which would work great if you had a 1866 Winchester chambered in the same cartridge. However, lWinchester came out with a new model - the 1873 - which was chambered in other calibers. The Army was looking for new models as well . . long story short . . the birth of the 1873 Colt . . which made the 1871/72 "open tops" pretty much obsolete.
If you look at the photos of those Uberti revolvers - the 1851 Conversion and the 1871/72 open top - you'll see a difference in the loading gate. The '51 conversion had the loading lever removed and an injector installed, etc. The conversion still utilized the rear sight notch in the hammer - the 71/72 had the sight affixed at the rear of the barrel - in front of the cylinder.
Today's reproductions are not always 100% "authentic" - they are available in different calibers, etc. If you buy a Uberti 1851 "conversion" or a 71/72 "open top" - the barrels will be bored and rifled to standard 38 special specs. - i.e. you can use today's .358 molds - today's 38 Colt Short, Long, Special (or whatever the revolver is chambered for). I load a lot of 38 Colt Short & Long - I like the history of both cartridges.
The repos are made to shoot today's standard ammo which meet SAAMI specs. I believe they should be shot with lead bullets though. Some may argue that the "open top" revolver ('51, 71/72) are "weaker" than say a 1873 or a Remington with a top strap. Let 'em talk . . there is nothing wrong with the open tops and they will shoot just fine.
I have one on my "to buy" list - just haven't decided which model yet. As you will see . . . some are made with Navy grip frames, some Army - some Navy octagon barrel . . some the Army smooth rounded ('61 type) barrel. I shoot a '51 C & B Uberti and have a preference for "navies". I'm leaning towards the Richards & Mason conversion with the full length barrel.
Study the photos and the descriptions. If you have any questions . . . give the places a call (Ubeti, Taylor, Cimarron) and they'll be happy to answer your questions. Good luck and have fun!