The Earth-Luna mass ratio would be the closest among any planetary moon to planet to one. ie, Luna would be the largest satellite in comparison to its planet.
Unlike every other planetary moon, it has a purely convex orbit. ie, it never loops its own orbit, and it never appears to backwards when drawing its orbit around the sun.
Since there is no other known example of binary planets, there is no need to distinguish these types. For now, "Moon" adequately encompasses the characteristics of this and other lunar systems.