I consider the "two in a calendar month" definition to be one that is traceable to an error which the offending publication corrected.

It's shown, historically, in the USA, since blue moons were being recorded by those interested, that blue moon meant third in a four moon season.

Then again, I'm someone who has to send out calendrical announcements based on the lunar cycle, and using specific names - where the first one after a seasonal change, the second one after, and the last one before the next seasonal change, all have names - thus, the third has no name, and needs one.