They are not really different because they are all electrical in nature.
Forces between ions tend to be a lot stronger than forces between molecules, because ions are formally charged, while molecules are electrically neutral.
Na+ Cl- (strong attraction between formal charges)
The following is an example of an intermolecular force. Below, each H-Cl molecule is electrically neutral (each Cl has 3 lone pairs of electrons not drawn in) Since Cl is more electronegative than H, the electrons shared between H and Cl are more likely near the Cl atom. This makes the Cl end of the molecule partially negative, and the H end partially positive.
The intermolecular force below is represented by the dotted line. It is an attraction between the "kind of negative" Cl of one HCl molecule and the kind of positive H on a different HCl.
H-Cl - - - - - H-Cl
It is electrical just like the ionic attraction, but since neither the H or Cl are formally charged, this dipole-dipole attraction is weaker.