Question

Distinguish between centre of mass and centre of gravity?

Answer 1

Mass is an intrinsic property of every body which is unaffected by external factors. The weight of a body however is the force it exerts on its support keeping it upright against gravity.
The "center of mass of a body" is the point at which the whole mass of the body is taken to be concentrated.

On the other hand, "center of gravity" is the point at which the entire weight of the body is taken to be concentrated.

If the body is so huge that the value of acceleration due to gravity has different values over its surface, the center of mass and center of gravity may not coincide.