One of the most important differences in the construction of firearms around the time of the American Revolution is the transition that was taking place between the musket and the rifle. Many people think they are the same thing but there is a world of difference.
The British forces were armed with the traditional musket, typically one called the "Brown Bess." A musket has a smooth bore (or inner barrel) and shoots a ball. The effective range of a musket was around 75 to 100 yards and it was not very accurate. This is why the British troops tended to group the riflemen together and shoot volleys, increasing the likelihood of more hits.
The rifle, which was becoming more and more popular in America, has a "rifled" barrel (with grooves cut into the inside that produce a spin) and shoots a bullet which, because of its shape and spin, is much more accurate at greater ranges. A good rifleman could hit his target at 200 to 300 yards, while experts could shoot accurately up to 400.
The advantage of the musket was that, with training, a musketeer could shoot up to 4 times per minute while a rifleman would probably shoot once per minute. Speed was being sacrificed for distance and accuracy.
This is probably the greatest change in the construction of firearms that was seen during the Revolution.
To learn more about the various military technologies and tactics used in the Revolutionary War, check out this podcast: