When I dug it, I thought I found silver, wasn't tarnished at all but after cleaning, clearly its a button. My research has led me to believe naval artillery?
The second one, a "great seal" button is WWI era, which can be dated by the black finish... Although they continued with that for a bit after the war there weren't as many during those years, statistically it was likely a war time issue.
To elaborate on NHBenz's correct identification of Great Seal button; the black finish was used from 1910-1923. The front of your second button does look like a Navy one. The back is what concerns me. It may be a modern Navy one. US Navy - Eagles - Waterbury Button
I found the navy one about 12" deep and it was at an old homestead. I'm still not sure. I'll clean more and see if I can id any lettering on the back. Thank you all