What are the differences between a magnetic and gravitational interaction

Classically, gravitational attraction is due to the masses of objects. It is inversely proportional to the square of the distances between the objects.

Magnetic attraction is due to the magnetism in objects which is due to uncompensated electron spins in certain atoms. The force due to magnetism less easy to put into one equation than gravity since magnetic fields can have different shapes, but the simplest one (the dipolar field) is inversely proportional to the cube of the distance between the magnetic dipoles.