Your bullet is a .54 or .58-caliber 3-groove ("3-ringer") Minie bullet from the civil war. Most (but not nearly all) 3-groove Minie bullets were yankee-made. The small groove encircling its top ought to be the mark of a ramrod, used in loading the bullet into a muzzleloader rifle. The ramrod-mark indicates the bullet was fired, but flew a long way without hitting anything before it ran out of energy and fell to earth without much damage. Or, the nose groove could be from a double-helix bulletworm, and the bullet's miss-shapenness is due to being stepped on. Need some closeup photos of the nose groove to know which of those two possibilities is the correct answer.
I think the other object is a fired 20th-Century shotgun slug.