What is the fundamental difference between the definitions of the two moons?

Answer

Their ruling definition—equinox proximity versus sequential position.

The fundamental difference rests in the ruling definition for each name: the Harvest Moon is based on proximity to the Autumnal Equinox, while the Hunter's Moon is based purely on following the Harvest Moon.

What is the fundamental difference between the definitions of the two moons?
astronomyMooncelestial bodyHunter moonHarvest Moon