The difference is there never was a Colt 1851 with a brass frame, let alone in .44.
Schneider and Glassick made an almost exact copy of the Colt 1851 in .36 with a brass frame.
So I guess it could be argued that the pistol in question is closer to the Schneider and Glassick than a Colt 1851.
The Griswold & Gunnison was similar but had a round barrel. The Leech & Rigdon was another close copy but with a round barrel and far as I know a steel frame.
I'm not aware of any "1851 types" made historically in .44.