Ball ammunition, also known today as full metal jacket (FMJ) ammunition, represents anything that is a non-hollow-tipped jacketed bullet or what the military uses as standard ammunition. Its name derives from the beginning of firearms, where muskets with large metal balls were used before the arrival of conical ammunition. The term probably came about because smooth-bore muzzle magazines used a ball-shaped projectile. This is the most consensual origin of the term.
However, that's not always the case, since sometimes ball ammunition is simply certain ammunition that was originally intended for a gun, and it's the standard charge for that weapon. In 1849, a man named Claude-Etienne Minie invented a new cylindrical-shaped ammunition that became known as the “minie ball”. I would say that the term FMJ originated on its side of the pond, where the British military probably still uses a ball in their ammunition boxes. The term FMJ only refers to anything that has such a jacket, and ammunition labeled “ball” is actually FMJ 99% of the time.
And also, the ball labeled with ammunition is usually the typical average load, and not Match, subsonic, lead-free, tracer or anything else. Military surplus will also have gunpowder, while foreign ammunition labeled as such from the past 50 years may have any type of gunpowder, but they are only using a U.