Actually, these terms are all operational and arbitrary, like "river", "stream", "creek", "brook"; or "metropolis/city/town/village/ hamlet". These are just terms of convenience, not a true physical taxonomy. Sooner or later you have to define purely arbitrary size limits to distinguish one from another. Trying to describe them precisely is only going to lead to confusion because the public will confuse the words with intrinsic physical differences.

After all, a gas giant, like Jupiter, has more in common with the Sun than it does with Earth. The solar system could easily be described as a binary star system, Sol and Sol B (Jupiter), each with its own retinue of planets. The terms "planet" and "satellite" should be deliberately ambiguous, like "world"