Actually that is not true:
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Moons orbit planets, planets orbit stars. That's the main difference. Size isn't a factor as a moon orbiting a large planet can be larger than a small planet. And not all moons are just balls of rock and some planets (mercury) are not much more than balls of (molten) rock.
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Several of Jupiter's moons have atmosphere.
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Things get a little confusing when we talk about binary-planet. I won't quote some of the defs I've read but leave it as the Moon is considered rather large by conventional standards.
