Both Union and Confederate cavalry used different types of saddles, with some generals even having custom saddles made for comfort and style.
Union Saddles: The main saddle for Union cavalry was the McClellan Saddle. It was lightweight, practical, and designed for long rides. It had a high front and back and was easy to adjust for different horses. Officers had slightly fancier versions of this saddle, with more decoration and padding.
Confederate Saddles: The Confederacy didn't have a standard saddle like the Union did, so Confederate cavalry used a mix of captured Union saddles, locally made saddles, and civilian saddles. Since the South didn't have as many resources, their saddles were often more rugged and less uniform.
Generals' Saddles: Generals from both sides sometimes used custom saddles for extra comfort. These were often similar to the standard ones but with extra padding or decoration. For example, General Lee's saddle was similar to the McClellan style but made more comfortable for him.
In short, while Union soldiers had the standard McClellan saddle, Confederate soldiers had to make do with whatever they could find, and generals on both sides often had fancier, custom saddles to fit their needs.
@aidenmac17 I don't honestly know much about Civil War saddles. With that said I recently acquired a copy of 'Confederate Saddles & Horse Equipment' which was highly recommended by several Cavalry collectors that I know. The following books might prove useful to you.