The first button has a very-wide flat back, so it's not a ballbutton. As a 2-piece button with a plain blank front, it is a civilian-usage button, not a military-usage button. It's backmark (maker's-mark) saying "D. Evans & Co. / Attleboro Mass" in tiny letters dates it from sometime between 1860 and 1880. However, this button's front appears to be plated with Nickel-Silver (also called German-Silver, and containing no actual silver), which indicates 1870s manufacture, not 1860s.
The second button is what button-collectors call a brass 1-piece "flatbutton." That type, having a plain front and no backmark, dates from the 1790s through the 1830s. At that time, the fledgling American button-making industry was unable to mass-produce enough to satisfy the demand from the clothing-making industry, so most of these brass 1-piece flatbuttons dug in in the US were manafactured in Britain.
