"Ball" is a military term for a normal inert projectile, that is, not anything special like tracer, armor piercing, incendiary, etc. Today, that means a full metal jacket, but the term was used in the lead bullet days as well.
"Hard ball" is an informal term used by target shooters, primarily shooters of the Model 1911 or its variations, to distinguish military type FMJ bullets from wad cutter, lead, soft point, or hollow point commercial loads. It is also applied to pistols ("hardball guns") set up specifically to fire millitary spec ammunition, which is harder on pistols than light target loads or light hand loads.
Jim