In button magnets the poles each occupy a side of the end of the magnet face and are separted by a groove. They're made from a single piece of material so don't suffer from differential expansion or contraction and are therefore more suited to some higher temperature applications than pot magnets. They're not as powerful as the equivalent pot magnet but have a greater depth of field (the distance that the magnet can attract over).
Note: don't mix up button and pot magnets (pot magnets have the poles arranged concentrically on the magnet face, one inside the other) as they behave differently and have different uses.