It looks like a S&W "New Model" Model 3, made from 1878 to 1915.
Uberti makes a reproduction:
NEW MODEL N.3 FRONTIER | Uberti Replicas | Top quality firearms replicas from 1959
S&W did a run in .45 Colt in 2002.
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The original "New Model" Model 3 introduced in 1878 was smaller, lighter and more concealable than the previous American, Russian and Schofield models and also reverted to the original locking system.
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I read an article awhile back that criticized S&W for not making the Model 3 in .45 Colt in 1875 when the government originally ordered it. S&W instead chambered them in the shorter .45 S&W Schofield round. Anyone who thinks that was S&W making a mistake doesn't understand black powder era cartridges.
You'll note the .44-40, 38-40, 32-20, etc, all have a tapered body and a slight shoulder, along with a substantial rim. The shoulder helped seal the case to the chamber wall quicker and reduced powder fouling in the chamber. The slight taper in the body ensures that as soon as the case moves aft on ejection, the entire surface of the case is out of contact with the chamber walls. The heavy rim ensured the extractor in a rifle or an ejector star in a pistol could get a good enough grip on the rim to get it started out of the fouled chamber - and black powder fouling is extensive.
The .45 Colt on the other hand was designed to maximize case capacity - the .44 mag of its day. It had straight, parallel walls, no shoulder, and a very small rim (smaller than modern .45 Colt brass). The small rim allowed for a smaller diameter cylinder on the Colt Single Action Army, for which the .45 Colt was designed. Since the Colt SAA used a rod ejector, there was plenty of ejection force available and there was no need for the common features normally found on pistol sized black powder cases.
That's why you won't find black powder era lever actions chambered in .45 Colt - they relied on an extractor, not a rod ejector.
Thus, when the US Army ordered the S&W Model 3 Schofield, S&W wisely developed a shorter version of the .45 Colt that was easier to eject due to the shorter length. The Model 3 used a top break design and a star ejector that made it fast and easy to load, but the star ejector design wasn't reliable with the full length case of the .45 Colt.
In 2002, with smokeless powder .45 Colt ammunition, it was no problem chambering it in .45 Colt.