So here you have two definitions of a blue moon but the one for a calendar blue moon does not describe the true meaning of a blue moon. Here's why:
The three little moons (Methone, Pallene, and Anthe) orbit at very similar distances from Saturn, and they have a dynamical relationship. Mimas disturbs the trio of little moons, and causes the orbit of Methone to vary by as much as 20 kilometers (12.4 miles). Mimas causes the orbit of Pallene to vary by a slightly smaller amount--but it has the greatest influence on the orbit of the moon Anthe.
Comets are really traveling relic icy planetesimals, the remnants of what was once a vast population of ancient objects that contributed to the construction of the quartet of giant, gaseous planets of the outer Solar System: Jupiter, Saturn, Uranus, and Neptune. Alternatively, the asteroids--that primarily inhabit the region between Mars and Jupiter termed the Main Asteroid Belt--are the leftover rocky and metallic planetesimals that bumped into one another and then merged together to form the four rocky and metallic inner planets: Mercury, Venus, Earth, and Mars. Planetesimals of both the rocky and icy kind blasted into one another in the cosmic "shooting gallery" that was our young Solar System. These colliding objects also merged together to create ever larger and larger bodies--from pebble size, to boulder size, to mountain size--and, finally, to planet size.