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Dipole interactions form between two molecules that each exhibit dipole moments (meaning that the molecules has uneven charge). So within the molecule itself it would be called a dipole moment, but with two or more molecules it would be a dipole interaction because the molecules with dipole moments are interacting with each other.
Dipole interactions are present between dipole moments. A molecule that has dipole interactions must have dipole moments, so yes a molecule can have both. Finally, ion-ion interactions (not ion-ion dipoles, I think is what you are referring to) are the intermolecular interactions that are present between charged ions.
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