ITS A SECRET
They look similar to the medal Rune got when she became a Dragoon - Magi writing along the outer rim (each of which says what the class is), four part compass in the middle. However, each one is a different color, not rainbow, and in the middle is a silhouette of the weapon that particular class is famous for.
Swordsman is red, with a sword obviously. Acolyte is a staff with a round crystal on top, and is yellow. Archer is green with a bow. Mage is blue, with an open book. Thief is purple, with a pair of crossed daggers.
Permanent classes are the ones with rainbow colored badges.