Belts are a meta classification that refer to a collection of Small Body objects in a stable orbit around a star or planet.
Circumstellar belts are individual bodies in orbit around a star. The difference between a belt and a disc tends to be that a belt is viewed as a collection of individual objects, whereas a disc is viewed as a much wider band of smaller particles which aren't considered individually.
A Belt can have moons. In this case these are major worlds (normally large asteroids) within the belt. Internally, the moon's distance is measured from the middle of the belt, so may be negative if it is on the inner half of the belt. 'Moons' that are part of a belt are called planetoids.