IIRC, I heard once that "blue moon" came from a widely used farmer's almanac in the USA in the 19th C. With no radios, digital watches, GPS, internet etc, farmers needed a way to keep track of the date, so as a regular check they indicated on a calendar when full moons would be, and if there was a second one in the same month, they coloured it blue.
Or that might all be b******s.