How does the formation of our moon differ from moons around other planets?
Most other moons are thought to have formed by accretion. Ours is thought to have formed by a giant impact.
There are actually three theories of our moon formation.
Giant impact hypothesis.
Co-formation theory. (most moons)
At present, the giant impact hypothesis seems to cover many of the basic questions, making it the best model to fit the scientific evidence for how the moon was created.