The first one is called a Half and Half button for obvious reasons because there are two different fabrics on it.
I have joined the seam with Cross stitches and then added some French Knots
The second one is a Ball button or sometimes called a Knob button.
I think it looks like an arthritic Sea Urchin but you can't see all the bumpy bits because of the way I photographed it.
I will make a better one later.