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:
"For the smaller craters, it's like if you're filling a bucket, eventually your bucket gets full, but if you keep pouring cups of water into the bucket, you can't tell how many cups of water beyond full you've gone. Looking at the larger craters at the subsurface might give us insight, because that 'bucket' isn't full yet," Dr. Soderblom added.
There was a time when Earth had no Moon. About 4.5 billion years ago, when our ancient Solar System was still forming, the dark night sky above our primordial planet was moonless. At this time, the Earth was about 60 percent formed, although it did have a differentiated crust, mantle, and core. This was a very chaotic and violent era in our Solar System's past, with planets first forming out of blobs of primordial dust, gas, and rock. During this era, frequently likened to a "cosmic shooting gallery", collisions between the still-forming planets were commonplace. Orbits were not as orderly as they are now.