Blue Moon is different from the monthly or seasonal moon names as it isn't restricted to a time of year. It is a movable feast. The older meaning may be wishy-washy and the newer one solid and technical, but don't let anyone tell you they have replaced one with the other. It's not rare to see two full moons in a month. That's every thirty-three months on average.
Months have different lengths, so the phenomenon moves around a bit.
If you think about it, it's a little like getting paid every second Friday and finding that some months you get paid three times instead of twice. Meaning is a slippery substance. I have counted six different meanings which have been carried by the term, and at least four of them are still current today. That makes discussion of the term a little complicated. Both phrases were used as examples of obvious absurdities about which there could be no argument.