During various dynasties, emperors worshiped the moon in autumn.
They did so in hopes of a plentiful harvest, rejuvenation, etc.
There’s also a story of a moon goddess, Chang’e, who got into a rift which caused her to flee to the moon.
She supposedly embodies healing, fertility, love, compassion, and grace, which can also be bestowed on those who worship her.
Whatever the moon does or does not mean to you, we’re looking at the same one.