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:
After a long and dangerous journey through the space between planets, the Cassini/Huygens Spacecraft reached Saturn on July 1, 2004. On December 25, 2004, the Huygens Probe was purposely liberated from the Cassini Orbiter. Huygens then began its historic descent through the dense blanket of golden-orange fog to at last lift the veil hiding Titan's long-hidden face.
The ring around the Earth eventually began to condense into blobs that then proceeded to merge and create a large and brightly glowing sphere--our primordial Moon. Our Moon would have appeared to be ten times larger than it does today in Earth's ancient sky--if anyone had been around to see it.