That type of button is called a rivet-button or "tack-button." They are used mostly on work-clothes such as coveralls, and blue jeans waist closure, because due to their "rivet" structure they can withstand much more strain than a sewn-on button.
Although most have a plain front, some have a design (such as stas) or lettering on the front.
They are mostly from the 20th Century to the present, but a few "Railroad logo" coverall rivet-buttons seem to date back to the 1890s. None are from the civil war era.