The weapons used in the Civil War were largely rifles, most commonly the 1853 Enfield and the 1861 Springfield. Rifle refers to the grooves in the barrel which imparts a spin on the projectile allowing for greater distance and accuracy. Thus even though Civil War soldiers did load through the barrel as you describe they still had rifles. Breech loading, repeating rifles became common in Union Cavalry by the end of the war. A famous description of the 1860 Henry Repeater is that "you could load on Sunday and shoot all week." Six shooters were common by the Civil War as Samuel Colt had been producing them since 1848, though generally only officers and cavalry would use them.