Your black-finish buttons are US Army "Great Seal of the United States" buttons. That type dates from 1902 onward. Your black-finish ones date from World War One or later.
Your eagle-on-an-anchor button appears to be a civilian Fashion button, specifically, a civilian-usage imiation of a US Navy button. Your ironbacked button with two unicorns (or whatever they are) also seems to be a civilian Fashion button.