No photo showing the button's back is visible when I view this discussion-thread.
The button's emblem, a wreath below several stars, immediately made me think it is a rivet-button. When you posted the second photo, showing the button "stands up" almost vertically on its own, that tended to confirm it is a rivet-button even without seeing its back. (As I said, no backview photo shows in this thread on my computer.)
Another term for rivet-button is a "tack-button." Here's a photo showing a (modernday) sales-packet of rivet-buttons/tack-buttons whose emblem differs from your button only in having 5 stars instead of 3 stars.