As its name indicates, a "Chicago Screw" rivet has a screwdriver slot on one of its discs. If there's no screwdriver slot on your rivet, it's an ordinary rivet. The size of your copper/brass rivet indicates it held two thick pieces of leather together. That type was used on a great many leather objects, and is very commonly seen on "antique" horsegear. Like nails and screws, there's no way to know with certainty whether a "generic" rivet was used on a Military object or a Civilian object... unless you dug it out of the bottom of a battle trench or a military winter-camp hut. If it was found in the woods or a field, it could be either Military or Civilian. And, there's no way to know whether it was lost in 1863 or 1903.
a Chicago screw is a two piece rivet that screws together...slot is optional...I have many swords that handles are secured with a Chicago screw, without slots for scewdrivers...
the Japanese would place a mon on the rivet...or smooth the surface for looks...