It is definitely the stripped-off jacket from a copper-jacketed lead bullet. More specifically, a "semi-jacketed" one... which means the copper jacket did not cover the lead bullet's front end. See the photos below, showing copper-jacketed bullets, fired and unfired, and sawed-in-half.
A related term for jacketed bullets is "Full Metal Jacket." (A famous military movie used that term for its title.) It means the jacket covers all of the lead bullet's body except for an opening in the base, where the lead core was inserted into the jacket.
The lead bullet's jacket is made of a thin metal sheet, not a casting, or "plated." See the sawed-in-half Full Metal Jacket bullet at far left in a photo below. A bullet's jacket is most often copper, but there have been brass, steel, and nickel jacketed lead bullets.
When a semi-jacketed lead bullet hits a semi-soft solid material, such as tree, or clay-type soil, sometimes the jacket catches/snags in the material and the heavier lead core of the bullet comes out of the jacket and keeps on going. The stripped-off copper jacket is what Tigerdude found. Note that its diameter is larger than the typical .24-inch cicil war musket/rifle percussion cap, whose dimensions were astutely provided in post #10 above by my esteemed colleague Charlie_P.