Although most folks don't know it, caliber does NOT mean the same thing as a projectile's diameter. Caliber is the diameter of the firearm's bore. For muzzleloading firearms (the projectile is loaded into the barrel's front end), the projectile was always a bit smaller than the bore. For breechloading firearms (the projectile is loaded into the barrel's back end), the projectile is slightly larger than the bore.
Examples:
Civil war breechloading Colt .44-caliber Revolver (bore diameter is .44-inch), the bullet is .46-inch in diameter.
Civil war breechloading Sharps .52-caliber Carbine, the bullet is .53 to .54-inch in diameter.
Civil war muzzleloading Springfield .58-caliber Rifle, the bullet is .56 to .57-inch in diameter.
Civil war muzzleloading Springfield .69-caliber Musket, the bullet (a ball) is .64-inch in diameter.
If CMartis' statement that his lead ball is "63 caliber" is incorrect, and the ball actually measures .63-inch in diameter, it is probably an "eroded" .69-caliber musketball. However, as MarkP, HomeGuardDan, and CSA2K indicated, some varieties of civil war artillery Case-Shot shells contained .64-inch diameter lead balls as antipersonnel balls. Therefore, knowing with certainty whether a .64-inch diameter lead ball is a musketball or a Case-Shot ball can be difficult. Often, case-shot balls were not PERFECTLY round. But I've examined many case-shot balls (taken out of cracked-open Case-Shot shells) which are definitely perfectly-round. HomeGuardDan mentioned a way to tell the difference... if you are finding artillery shell fragments where you found the lead ball, it is probably a case-shot ball.