As a general posit - a moon should be notably smaller than it's primary. And by "smaller" I really mean "less massive". If we assume that the moon is made of stuff similar to the planet, this also generally means it is of smaller size, but one can construct edge cases.
People think in terms of a moon orbiting a planet. That is technically not quite correct. Both the moon and the planet orbit their common center of mass (aka "center of gravity"). If the planet is much heavier than the moon, the center of mass is probably within the body of the planet, so it looks much like the moon orbits the planet. For our Earth and Moon, the center is about 1700 km under the surface of the Earth (so, some 4700+ km from the center of the Earth itself).
If the two objects are of equal mass, the center of mass is right between them, and it looks more like the two objects orbit that point, or that they "orbit each other".
And, clearly, if the moon is actually more massive than the planet, you've mixed up which one is the primary, and which is the satellite.