The definition for a moon can be very similar to a planet:
Planet:
1. orbits a star
2. large enough to be round
3. orbitally dominant
Moon
1. orbits a planet (instead of a star)
2. large enough to be round
3. orbitally dominant (around the planet)
Just like for planets, rule #3 would help distinguish between dominant objects and belt objects.
I have no idea what the orbital data of moons around planets is like, but I expect that it's a very similar dynamic. The "cleared the orbit" phrasing of the IAU would seem especially apt for the tiny shepherd moons of Saturn's rings.
In those cases, we can see the "clearing" action is still in progress! Of course, those moons would fail rule #2, so they might be better named "moonlets" or something similarly descriptive.