Allow me to explain the concepts of and potential before this.
Electrostatic force is a conservative force, i.e. done by an external agent (force equal and opposite to the electrostatic force) in bringing a charge q from point A to B is independent of the path it takes to reach B from A.
Now, coming to electric potential energy, the potential energy of some charge configuration at some place in an external electric field (The field must not be the one the test charge produces), is the work done by an external force (equal and opposite to : so that is zero, speed may be considered infinitesimally small.) in assembling the charges in their respective locations from infinity.
The difference in potential energy (between two points) is simply the work done by an external agent in displacing the charges from the initial point to the final point with infinitesimally small speed.
Since, work done is involved, the magnitude of the charges are also involved and thus potential energy of a charge (or any charge configuration) is pretty much dependent on their own magnitudes as well as on present there.
Now, let us see what electric potential is,
It is the work done per unit charge by an external agent (equal and opposite to the electric force, as before) in assembling the charge(s) at their locations from infinity. It is the characteristic of the electric field at that point and is pretty much independent of the value of the test charge.
So, in a nutshell, the potential energy depends on the charges themselves whereas potential at a point is the characteristic of the field. We can alternatively use potential (scalar) at every point to describe the strength of the field instead of using the electric field vector.
It is again to be noted that when difference in potential and potential energy is involved (between two points), it is only the difference that is physically significant, not the actually coordinates of the points. This follows form the fact that electromagnetic force is conservative.