What is the difference between rotational, circular and curvilinear translational motion?

See, curvilinear motion refers to a motion along any curved path ( as the name suggests) but not along a straight line path.The radius of that curved path is not constant , but it varies. While in case of circular motion , there is a force acting towards the centre of that circle resulting in motion of that particle along a circle.

Note that circle is a special type of curve having constant radius.

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