By the 1858 regulations, the forage cap was part of the fatigue dress, which was not supposed to be worn on parade or in battle. The Hardee hat was the campaign hat. But as time went on, soldiers started wearing the fatigue headgear at all times because it was the most comfortable and practical, and it became the most common and iconic style of dress. There were also stiffened shakos for parade dress in the Union army, but you definitely (hopefully) won't see those at battle reenactments.