The main difference between these types of motion is that circular motion is a special case of rotational motion, where the distance between the body’s centre of mass and the axis of rotation remains fixed.
In rotatory motion, a body rotates on its own axis (passing through it) while in circular motion, any body/particle moves on a circular path with centre outside the body.
For Example:
If a ceiling fan is running, we say the fan (as a whole) is rotating, while any part of it (like the end of a blade) is moving in a circular path around the central axis.
OR
The earth is rotating around its own axis, while we the humans, the animals, and everything else is undergoing circular motion around the earth’s axis of rotation