Thank you all for your time. 

Micheal was very kind and explained me some infos. 

Maverick said
I’d be curious to know what the barrel markings look like as well.

  

There is an “expert analysis”, written in Italian, that highlights some peculiarities. I will try to translate it in English to answer your questions. 

…) The imprinted wording allows to identify the weapon “MODEL 1892” and the patent date “PAT OCT 14 1884” (….) (…) From examining the weapon it is clear that the bore of the barrel is smooth” (…) “The weapon has dimensional characteristics of some details (see King loading gate) which do not allow it to chamber 40 44 caliber cartridges” (….)(….) the dimensions of the leading gate are smaller in relation to the 44 40 caliber stamped on the weapon” (…) 

(…) Special cartridges have a shortened cased, loaded with a reduced dose of black powder, 20 grains (1.296g) and loaded with shot of 7 ½ of the American number for a weight of ½ ounce (14.2g), contained in a capsule called sabot. This shot cartridge are approximately 28,6mm (1.5 cm shorter than the original one).”

Sorry if this translation is not accurate, but most of the specific gun-related terms are not of common usage.

It’s part of my father collection that we are donating to a museum here in Italy, but we will probably keep this one and some others. 

Zebulon said
Doc Carver and other exhibition shooters were fond of smooth-boring the 44 1892. Even old Top admitted to doing so very early in his career when he traveled with a Mexican circus, pedaling a unicycle around a circus ring in the big tent, breaking thrown glass balls with dust shot.  The circus owner was happy until the tent came down and he saw all the tiny holes in the canvas. Top never used shot cartridges after that and all his Winchester performances were straight up.  

I doubt the barrel on that 92 is a replacement. Any shade tree blacksmith with a lathe and a self-following tool could remove rifling. 

  

Thank you, very interesting ! Can I ask who “old Top” is? 

Martina