Normally, when something is referred to as a cap it is a typically headgear that has a visor and no brim such as a kepi. A hat has a shaped crown and brim.

Numerous examples can be found in the various books on the American Civil War but great books for examples are in Time-Life books "Arms and Equipment of the Confederacy (Echoes of Glory)," and "Arms and Equipment of the Union (Echoes of Glory)."

I hope this helps.

Respectfully,

Gerald D. Hodge, Jr.
War Between the States Historian
M.A. Military History - Civil War Concentration
Historian: 39th Georgia Volunteer Infantry Regiment