.44-40 with a 10mm cylinder?
Not likely, since 10mm = .40 cal.
Ruger has made some .38-40 x 10mm convertibles, also a batch of .38-40 x .40 S&W, I think; the .38 WCF (.38-40) being a true .40 caliber.
Any road, the .44-40 is a blackpowder round first offered in the 1873 Winchester, shortly followed by the Colt SAA and a number of others cashing in on the popularity of the first centerfire Winchester repeater and its ammo. Current ammo is loaded with smokeless to blackpowder ballistics of 200 grains at maybe 800 fps in revolver, 1300 fps in rifle. Even less in Cowboy ammo. The .38-40 is the same case necked down, firing a 180 grain bullet about the same velocity. There used to be some heavier factory loads but they have been dropped as not being very useful vs .30-30 etc and not safe in the oldest guns. Handloading can soup it up, but only a little, brass and chambers are thin. Of course a Ruger will stand a lot more souping up than a Colt, but for heavy loads you would be much better off with a .44 Magnum or .45 Colt.
There are a fair number of .44-40s (and some .38-40s) being shot in Cowboy Action Shooting; some because it is traditional and some because it is better suited to blackpowder loading. I use it myself, largely because I got a good deal on a '92 Winchester .44 and got matching sixguns. Cowboy is about the only practical use for it (them) these days. Ammo is neither cheap, plentiful, or powerful. The thin brass and bottleneck shape make it more trouble to handload than, say, a .45, too.