The Super Boss is one that often exists outside the normal plot of the game, and requires quite a bit of conscious effort to get to. Its difficulty is usually much beyond that of the "story line" final boss. Occasionally, games may have more than one Bonus Boss. The key point here is that they make up the most difficult enemies in the game, and that includes the actual last boss of the game. Sometimes, the player may acquire an Infinity+1 Sword or ability once they beat this extraordinarily difficult enemy, but it's usually a Bragging Rights Reward. Anyone who can beat the Bonus Boss has proved they don't need them, unless it's to get to another Bonus Boss even harder than the previous one.
They are primarly fought in Labyrinth of Chaos (Micaela, Lucifina) or dungeons (Nanabi, Sphinx) and can be powered up version of normal bosses.