Your ancestor's unit was in the Union army, right? I only have info on the 5th Ky. Inf. CSA.
But to answer your other question, during the Civil War, traditional cavalry units were organized and fought on horseback, whereas mounted infantry units were organized and equipped (more-or-less) as normal infantry, but they used horses for transportation. Upon reaching the scene of action they would dismount and fight on foot as infantry, often using normal infantry weapons.
As the war went on, these distinctions tended to blur, especially since many cavalry units started fighting more like infantry, and some were even armed more like infantry. Confederate cavalry commanders like Morgan and Forrest learned quickly that traditional cavalry weapons like sabers and pistols weren't as useful as infantry weapons, and traditional cavalry tactics like mounted charges were mostly obsolete in the day of the infantry rifle-musket. It didn't take long for most cavalry units on both sides to start using their horses mainly for transport, while fighting on foot with rifles and carbines.