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.
Out of curiosity, why did you say planetary moon? Is there any other kind?
Dwarf planets sometimes have moons (e.g. Pluto)
Some large asteroids have moons too.
this leads to the question: are they still considered a moon when the barycenter is in the space between them?
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.