No, most did not.
Revolutionary War muskets were flintlocks with smooth barrels, firing round balls. Rifles existed, but most armies did not use them, or at least used them sparingly. Napoleon did not allow rifles at all in his armies, for example. The problem with rifles is that the lead ball has to fit tightly in the barrel so that it grips the rifling (grooves in the barrel) and spins, which makes the ball more accurate. Black powder very quickly fouls the barrel, so reloading a muzzle loading rifle after a few shots gets more and more difficult. Eventually the powder fouling gets so bad that you can’t load the weapon at all. Fouling is no big deal if you are out hunting and can clean the barrel after a few shots, but you can’t exactly stop in the middle of a battle and tell the enemy to stop firing so that you can clean your barrel. Black powder also makes a lot of smoke, so much so that long distance firing on the battlefield wasn’t really much of a thing. After a couple of volleys you couldn’t see much at a distance through all of the smoke.
There were two changes made to muskets between the Revolutionary War and the Civil War, both occurring around 1820 to 1840-ish.
The first change was switching from flintlock to percussion lock. A flintlock has a piece of flint that literally strikes a piece of metal to make a spark. This ignites a small amount of powder in a small pan, which sends flame through a small hole into the barrel and ignites the main charge. If it’s wet outside, your flintlock goes click and doesn’t fire. If your flint isn’t in good condition, your flintlock goes click and doesn’t fire. If the metal piece that the flint strikes (called the frizzen) is dirty from powder residue or if you didn’t clean it well enough, your flintlock goes click and doesn’t fire. A percussion lock uses a small metal cap containing mercury fulminate. The hammer strikes this cap and the mercury fulminate explodes and sends flame into the barrel through a small hole and ignites the main charge. If it’s wet outside, no biggie. If you didn’t clean your weapon very well, no biggie.
The second change was the invention of the Minie Ball, which despite the name, is actually bullet shaped and not a round ball. The bullet isn’t flat on the back end like a modern bullet, and instead is hollowed out. The idea here is that you make your Minie Ball a bit undersized so that you can easily shove it down the barrel even after the barrel has been horribly fouled with powder residue. But then when you fire the gun, the hollowed out bit causes the back end of the bullet to flare out like a skirt so that the expanded bullet now grips the rifling very solidly, which makes the ball spin like a modern bullet. Civil War muskets were therefore rifled.
Smooth bore muskets always fire curve balls. The round ball will contact the sides of the barrel randomly as it travels down the barrel, which will make the ball spin in a random direction. The round ball will go straight for roughly 50 to 75 yards or so. After that, which way it goes is anyone’s guess. They used to say that you could stand 100 yards away from a single musketeer and not fear getting shot by him, which isn’t quite true but you get the point. A Civil War musket was much more accurate. A Civil War era musket firing Minie balls can hit a man sized target up to about 600 yards away, so they compare pretty well to modern rifles as far as accuracy goes.
The change from flintlock to caplock and the change to rifling the barrels seems like a couple of fairly minor changes, but these ended up being significant on the battlefield. The increased range combined with better tactics made charges like Pickett’s Charge at Gettysburg suicidal. That charge would have worked in the Revolutionary War. At Gettysburg, it failed miserably, and when Pickett was ordered to reform his men he replied that he had no more men.
Revolvers in the Civil War looked a lot like modern revolvers, but they were cap and ball revolvers and functioned more like miniature muskets. You loaded powder and a round ball into the front of the cylinder, then put percussion caps on the back side of the cylinder. You didn’t just stick the whole cartridge in at once like a modern revolver.
Metal cartridge weapons did exist, such as the Spencer Rifle and the Henry Rifle. These were very expensive to produce and the ammunition was also very expensive to produce, so they saw limited use during the war. They were often issued to cavalry units, while main infantry units carried muskets. Cartridge rifles increased the rate of fire from 3 or 4 shots per minute to 10 or 12 shots per minute, and they often proved their worth on the battlefield. For example, at Gettysburg in the Civil War, the Confederates first ran into a cavalry unit armed with repeating rifles. The rate of fire made the Confederates think that they were facing a much larger force than they actually were at that point. If the Confederates had realized that they were facing a much smaller force, they probably could have charged and overwhelmed the Union forces and dramatically changed the outcome of that battle. Instead, the Confederates waited for reinforcements, which allowed the Union time to also get reinforcements.
Paper cartridges of the type where stick the entire cartridge into the weapon were used and experimented with. Brass cartridges really didn’t take off until the 1870s, when improvements in the technology to make brass allowed brass cartridges to be made inexpensively enough to be practical. The U.S. army immediately switched to cartridge rifles after the war, so they recognized the improvement that brass cartridges made on the battlefield.
Civil War muskets also used paper cartridges, but these were not inserted in one piece into the weapon. Instead, the soldier would bite the end off of the paper cartridge (having enough teeth to do so was actually a requirement for enlistment in the war), pour the powder from the paper cartridge down the barrel, shove the Minie ball (which had been in the paper cartridge until the soldier bit it off) down the barrel, use the ramrod to ram the ball all the way down, then flip the musket around, take out a percussion cap from a box on his belt and put it on the musket’s cone, then fire. Then repeat the whole process, while the enemy is constantly shooting back at you. Fun. The paper cartridges meant that the soldier didn’t have to measure out powder from a flask, so that sped up the loading a bit, but still it was slow and cumbersome. Soldiers were required to be able to fire 4 shots per minute, which using a musket is moving very quickly.
FWIW, the Civil War musket was the worst standard infantry weapon to be shot with in all of history. The Minie Ball was a huge slug of lead (about 500 grains, compared to a modern 5.56 bullet which is about 50 or 60 grains) moving at just barely under the speed of sound. It made worse wounds than the round balls before it and worse wounds than the cartridge weapons that followed it.
I own both Revolutionary War flintlocks and Civil War caplocks, but I shoot at paper targets and don’t do reenactments, so I can’t comment on the safety procedures that they use.
A Revolutionary War musket doesn’t have sights on it, though you can aim it by using the tang screw (the screw that holds the back end of the barrel in place) and the bayonet lug as sights of a sort. The Springfield musket from the Civil War has a two leaf flip-up sight, so with both leaves down it’s set up for 100 yards, then you have a 300 yard leaf and a 500 yard leaf that you can flip up. The British Enfield musket (2nd most popular musket during the Civil War, used by both the North and South) has a ladder sight that goes from 100 yards to either 900 yards or 1200 yards, depending on when it was made. My experience with the Enfield is that anything you hit beyond 500 or 600 yards or so is pure luck, so those sights are a bit optimistic. Beyond 500 yards they were probably intended to give you a rough angle of elevation to fire in large volleys rather than to be used for actual single target aiming.
To put it in perspective, a Civil War era rifle-musket is just as accurate as a WW2 era rifle. The musket is just incredibly slow to reload. You could fire off all 8 shots from an M1 Garand, reload the next clip, and fire off 8 more shots in the time that it takes to fire 1 shot and reload the musket.