Sounds like your in for a day or two's worth of fun.
The shiny pistol with the engraving is a 1851 model. You can tell the 1851's by noticing they don't have the streamliked look of the 1860.
They also have a pivoting loading lever that rotates around a screw and it has a screw that connects the ram to the loading lever. The 1860's have a "creeping" loading lever that uses teeth engaged with holes in the barrel to make it move the ram.
Colt never made a 1851 in .44 caliber. All of the 1851's were .36's.
The engraved .44 caliber 1851 is something dreamed up by the Italians.
Don't let that get you down though. The .44 caliber 1851's with a steel frame like yours are excellent guns and great fun to shoot.
Their slightly smaller grip and balance in my opinion makes them even a bit better than the big 1860 Army.
Actually, my first cap and ball revolver was a steel framed Colt 1851 in .44 caliber. I really liked that pistol!!! Unfortunetly, my brain took over my common sense and convinced me to sell it because "it wasn't like the original Colt 1851". ( I was getting into the "everything MUST be just like the original" mind frame.)
That's the only reason I sold it and after it was gone and I had a proper, .36 caliber 1851, although the .36 was fun to shoot I missed my big "44".
Anyway, I can see your on the road to ruin. First one, then two, then........ It never ends.