I don't think the buttons are old military. There are reference webs sites out there but I am not home to get them for you. You make try Google as mentioned.
I believe they are old military buttons, the second one I would say is a general service button dating back to the civil war. U didn’t get a lot of response, maybe relist in the what’s it forum. Congrats !!
Your first button is a General Staff one and the second is a general service one. The staff button dates from the late 1850s-1860s and the general service one dates from 1854 to about 1870. As for value, I don't think they will bring much. Maybe $5-10.00 on the worn general service and $10-20.00 on the staff.