No doubt in my mind...the bullet 'looking thing' is indeed a bullet. It appears to be a lead cast round nose hollow-point design. The 'decorations' on it are cross hatching in order to retain bullet grease similar to how the cylinder wall on an engine is cross hatched to retain oil. If you look closely, you can see the land and groove marks from the bullet being shot out of a rifled barrel.
Just as a wild guess...I'd take a shot that it is a .38 bullet shot from a revolver. I've done a lot of bullet moulding, reloading and shooting and there is no doubt in my mind it is a bullet. As I said, my hunch is a .38, from a revolver.