Is the potential in "potential difference" the short form of potential electric energy?
It's a short form of electrostatic potential difference, which is the difference in the electrostatic potential between two points.

The eletrostatic potential is a field (a value associated with each point in space) that indicates how much energy would be required to put a charged particle at each point. But there is no energy associated with it until you also introduce that charged particle. 

Another way to think of this is that the electrostatic potential energy (of some configuration of charges) is the energy associated with the arrangement of those charges in an electrostatic potential. But the potential, and the potential energy are two separate things and you should be careful to understand how they're separate and how they're related.