The smaller ring could be a crush washer from an old spark plug. Hard to say for sure as there are 100 uses for an item like that...
If you'll post a few more angles of the larger ring I'll see if I can give you a clue. Please put a common item in the pics to indicate size. My first thought was "napkin ring". But it looks fairly heavy. Is it cracked or is it made with the split? Any spots or edges with significant wear?