It's an incuse design so the design you see on the front has been "pushed" into it from the back. So it's identical, one side "popped" out and one side pushed in.
If it's very thin but hard (not foil-like) copper or brass— and if there is no attachment point on the back, where a shank/eye has broken off— then it may be the die-stamped "face" for a three-piece gilt dress button, with the front and back held together by a separate rim, as on "staff" buttons. Also, some wooden and composition dress buttons had medallic or embossed disc inserts; so, it could be from one of those.