There are some claims that the moon is not a sphere but a flat disk. A spheroid moon should look more like a ball when illuminated by the sun from the side.
The reason why the moon looks so flat has to do with the roughness of his surface. The moon with his craters has a very rough surface. Rough surfaces like ceramics or the moon reflect light more evenly distributed than smooth surfaces. This is illustrated by the following simulation, which uses mathematical models of surface light reflections.
The sphere on the left has a smooth surface, the one on the right has a rough surface. The "moon" on the right looks flatter than the one on the left, like in real life.
The scene is illuminated by a white light from the upper left infinite far away, simulating the sun, and a dimmed blue/white light from the front, simulating the earths reflection.