Just an educated guess ...
All early firearms fired a smooth lead ball.
Even when the rifled barrel was invented, they continued to use a lead ball wrapped in wadding to provide some contact with the rifling so that spin would be imparted to the lead ball.
Accuracy was given a big boost when, according to Mail Call, a French military officer named Minie invented the pointed lead bullet with rings at the base of the round which grabbed onto the barrel rifling. US soldiers called it the "minie ball", even though it was not a sphere.
A firearms glossary I came across on the internet said [the term "ball" is most commonly used in military terminology and was originally a spherical projectile but now is generally a fully jacketed bullet of cylindrical profile with round or pointed nose.]
Putting these two items together, and knowing the military's tendency to abbreviate, I would guess the term "minie ball" was eventually shortened to just "ball".
When the metallic cartridge came into common use, the bullet was initially still just solid lead. When nitrocellulose (smokeless) gunpowder was invented and bullet velocities increased, cupro/nickel jacketing was put over the lead core to increase the solid lead bullet's penetration characteristics. With greater ammo velocities came more tinkering and other types of rounds were invented, such as armor piercing and incendiary, and I would guess they continued to use the term "ball" to describe a cartridge in which the bullet was just a plain, solid anti-personnel projectile.
Sound plausible?