If you have a proper planet-moon system, the moon “falls away” from the sun during part of its orbit – the moon’s orbit is, part of the time, convex toward the sun. A moon’s orbit is always concave toward the planet it orbits and the planet’s orbit is always concave towards the sun it orbits.

However, for the Earth-Moon system, both orbits are always concave towards the Sun. If you were to plot either orbit on its own, the orbit would form a circle with wobbly edges – it just doesn’t look that way in conventional pictures.

However, people are happier calling the Moon “a moon”, so who am I to argue?