The force between atoms of the molecule is called interatomic force.

E.g.The nucleus and electron cloud of a molecule is binded by electrostatic force. 

Intermolecular force is the force between the molecules of the substance is called intermolecular force.
There is a dipole-dipole interaction between the molecules.

Adhesive force is the attractive force between two unlike molecules. They are caused by forces acting between two substances like electrostatic force (attraction due to opposing charges), mechanical force etc. 

E.g., Force of attraction between gum and paper.

Cohesive attraction or cohesive force is the force of attraction between same types of molecules sticking together.