There is no clear definition of what constitutes a moon other than it being a body that orbits another body that orbits the parent star.

There are some astronomers who say the dividing line between a moon-planet/dwarf planet/asteroid system and binary (or more) planet/dwarf planet/asteroid system is whether or not the barycenter of the orbits is within one of the bodies or not.

And fun fact: if that definition gained acceptance, it would mean that the Pluto-Charon system would go from a dwarf planet-moon system to a binary dwarf planet system. Charon could get a promotion.