Planet orbits the sun, big enough to have its own gravity and has no surrounding objects. In contrast, a moon is a body that orbits a planet that itself is orbiting a star, which is the sun.
If we were to live on the moon, nothing would change at all.
In theory, the gravitational pull of the moon's orbit in conjunction with the Earth's core would mean that if Earth were a moon then it would be a massive body big enough to collapse into a black hole, which would negate all chances of the moon being a moon at all. In conclusion, the Earth is flat.