I was going to say button before your second message. Yours looks like to have been the
centre piece - first image with a plain back, and second with a horse head. There were some
buttons made with a standard backing, with a loop behind and in front an open part with
a rim round, then into that could be inserted any design needed. Not sure of the technical term
but it was made in two parts then when the middle (yours) was inserted then the outer
part was folded round it to keep it in place. So rather than make a whole button with just one
design, the backing was made many times, and individual designs for the middle could be added.
Still could be something else entirely of course.