The sum of Electric Potential Energy for a matter particle with an electric charge, or of a deposit of such matter (like a capacitor).
What is the source of your definition. Normally, electrical potential, or voltage, between two points is defined as the work per unit charge required to move the charge between two points. For a capacitor where the electric field $E$ between the plates is considered to be constant, the electrical potential, $V$ is
Where $d$ is the distance between the two plates. Electrical potential energy is the energy that a positive charge $Q$ acquires when moved from the negatively charged plate to the positively charged plate (or equivalently, when a negative charge is moved from the positively charged plate to the negatively charged plate) and is equal to $QV$ or for the capacitor $QEd$.
Is electric potential just the sum or measure of Electric Potential Energy for a given unit of matter with electric change?
They are related but they are not the same. Electrical potential $V$ is not the same thing as electrical potential energy. For a capacitor the electrical potential between the plates is $Ed$, and the electrical potential energy acquired by a charge moving from one plate to another against the direction of the electric field is $QEd$. Electrical potential is work (energy) per unit charge. Electrical potential energy is work (energy).
For gravity the analogy is the gravitational potential energy of a object of mass $m$ at a height $h$ near the surface of the earth has potential energy with respect to the surface of the earth of $mgh$. On the other hand, its gravitational potential (work per unit mass in this case) is $gh$.
Hope this helps.