The muscles that are used when snapping a football are all in the arm. More specifically, the forearm muscles are heavily used.
The whole body is actually used to do an underarm throw. However, when it comes to arm muscles, the latissimus dorsi is the main muscle used in underarm throwing.
Throwing a football in a game would use the deltoid muscles. I belive it is used in basketball aswell when playing a shot.
Many muscles are involved in throwing a dodge ball. Your back muscles, all of your arm muscles and some of your stomach muscles. Even muscles from your legs may be used depending on how hard you are throwing it.
most importantly your calf muscles
Most of them.
A kicking football is essentially a brand new football that is fresh out of the package. A throwing football is a "broken in" ball that is more used and easier to handle.