Seems to me that they mostly had smooth bore muskets and such in the decades prior to the Civil War, and most of those used percussion caps, which had replaced the earlier flintlock, a device which did not work in the rain. A percussion cap does work in the rain, but only provides one shot. It was used to fire a round ball.

Smooth bore firearms were necessarily rather short range and innacurate, compared to rifled barrel weapons which have grooves that cause the bullet to spin, greatly improving directional accuracy.

Rifled barrels had been around for awhile, but were not as common as smooth bore in the early to mid-1800's, I think. During the Napoleonic wars the British had rifle companies with rifled barrel guns, like the troops shown in Sharpe's stories. They were deadly accurate snipers, compared to the very innacurate firing guns of troopers in the main battle formations.

There were various pistols with revolving chambers, permitting several shots before the Civil War, and some rifles that had a similar arrangement. Tremendous progress was made in improving all these weapons during the Civil War, leading to modern cartridges, repeater rifles (like the Winchester carbine), chambered magazines that held a number of cartridges, and even gatling guns (the first real machine gun).

And that's my vague summary of a subject that I know a little about, but not a lot. I've probably got the details rather mixed up here and there.