You did not say anything about the size of the balls, which is hugely important in relic-ID efforts. Based on the apparent size of the balls, using your thumbnail for size reference, they are not grapeshot balls or any other type of Artillery projectile. The smallest iron Artillery projectile balls were about .56-inch in diameter. Yours appear to be smaller than than, when the thickness of the rust-crust is subtracted.
But as I said, I had to guess-timate their size, based on your thumbnail. Use a hammer to knock ALL of the rust-crust off one of them, and then tell us its PRECISE (hundredths-of-an-inch) diameter measurement. If an iron ball is smaller than .56-inch, it's not an artillery ball.
