The metal part doesn't look like it's been in the ground very long, while you bullet shows lots of patina. The knurling in the grooves of the bullet makes it a more modern bullet but the patina says it could date back to the early 1900's, late 1800's. As far as the other being a gun part, it's not part of any gun I'm familiar with, but there are modern guns with all sorts of stuff on them that I have no idea, perhaps some younger, more modern fellow will know more. The part has what looks like bluing, which is the finish on metal parts of guns, but it's stamped out, not machined, therefore I have doubts, but what do I know, the world passed me by several years ago.