Interaction Energy vs Force

I'm having a hard time determining the relationship/differences between interaction energy and forces. Say we have a system of two charged particles. Each particle will exert a force on each other (from Coulomb's Law), but also defined is an interaction energy between the two particles given by Coulomb's Law multiplied by the distance between them (reducing the $r^2$ term in Coulomb's Law to just $r$).

How are these concepts related? What is the correct way to interpret the interaction energy?

The force is just the gradient of the potential energy. So it's not true that the energy is just force multiplied by $r$. It is the integral of the force w.r.t. $r$, which gives you the $1/r$ dependence.