Federal Kepis
There are distinct differences between the US forage caps of 1858 and the kepi, often referred to as a Chasseur cap. Although both caps are an effort to do the same thing, make a lighter and more serviceable piece of headgear without the need for stiffening, the dress/work cap of our US army before the civil war was called a shako, a tall, cylindrical cap of cloth over stiffened felt or pasteboard. It wasn’t until 1872 that the US issued a kepi, which looked markedly different from the kepi of the civil war era.
US Indian War Kepi		US Kepi
At the time, it was usually a state or volunteer item purchased from manufacturers of private enterprise. US Commissioned offices were required to go to establishments called military furnishers to make their purchase within the guidelines of the US War Department. Great latitude was afforded in the details of manufacturer but all fit into a defined bracket of construction. A kepi consisted of a stiff band of paste board (no reeds or welts); a lacquered, stiff, flat, square visor, and a disc top made of fullers board.
Few had bodies that were so generous as to flop over the visor. The Kepi was a French effort to make a more easy to produce version of the shako. Americans in the south preferred the kepi over the forage cap and it became a predominate enlisted piece of headgear. Union officials displayed their rank via the "Austrian knot," a hat braid that was of either gold or black, silk, soutache.
Visors were almost always of leather that could either be unbound or have the more expensive braiding over the edge. As a rule, they were nearly always flat and square-shaped. Visors were also "glazed" with lacquer to make them waterproof and very glossy.
In the case of the private vs. the officer, even in volunteer regiments, the differences depended upon expense in details of manufacture. A cap for a private soldier of a volunteer regiment would usually be less expensive than that of an officer. The interior wouldn't have a quilted lining, cheaper materials would be used, and the visor would be unbound.  However, having said this it depended largely upon the economy of the state and the desire of the individual to show his ability to purchase, as in the case of an officer.
Some volunteer groups also used soutache or welts to elaborate uniform distinction. Colors and details depended upon state or rank military tradition.
14th Brooklyn Officer		U.S. Kepi