Unlike the International Astronomical Union (IAU) I think that we should define the celestial bodies by their physical properties. I also think that there is but one Moon. Other planets have “satellites”. The Earth’s satellite is the Moon. It does have many artificial satellites as well.
The Sun has many satellites as well which we know as Planets. We know them as Planets, not “Earths” though some call them “Worlds”. I think that some people like to consider “Earth” to refer to the Physical Body of our planet and use “World” to refer to the people and ecosystem including all our civilizations and cultures and biodiversity and stuff. So “Worlds” would perhaps be used similarly for other planets too….
However the Earth has a natural satellite called “Moon” or “Luna” or a number of other names depending on your language and culture. Mars has two natural satellites called “Phobos” and “Deimos”. Venus has no natural satellites and neither does Mercury. Jupiter and Saturn have a plethora of natural satellites, while Uranus and Neptune have them as well. Even Pluto has one whether you call it a planet or not. Asteroids, planetoids, dwarf planets, or whatever you call them — some have natural satellites. It is simple. The Sun has natural satellites and we call some of them planets.
But we should not call other satellites – “Moons”. We have a satellite called the Moon already!