Comes from the days when ammo was...
a premeasured bit of powder (black) and a loose ball to ram down the barrel on top of it.
It comes from the military, of course. Civilian shooters had to measure their own black powder. (Many probably had pre-measuring devices... another story.)
This was before the days of "specialized" ammunition; tracers, armor piercing and the like. When ammo became cartridge-ized (pardon the construction) the term stuck, although there was still no other ammo types... maybe blanks.
With the introduction of other ammo types, "ball" retained the concept of what a plain old ball did in the old days. In modern useage, ball ammo is ammo that doesn't do anything special, other than shoot.
Up until 1974 that I know of, .22 lr for target shooting (non jacketed) was officially listed as "ball". So was 158 RNL 38 Special stuff.
By the way, armor piercing ammo is in fact "Full Metal Jacket", but is not "ball". What is normally referred to as FMJ (used as anti personnel) is "ball". It is more a definition of function than form.