Potential difference

Potential at a single point is only ever a number relative to a zero you chose. Potential difference is not, and that is why it is the quantity physics actually uses.

The AP definition. EK 10.5.A.3 in AP Physics 2, matched by EK 9.2.A.3 in C: E&M, describes it as the change in electric potential energy per unit charge when a test charge is moved between two points. The sheets carry the consequence directly:

Read your equations again and it is always the difference. Ohm's law is printed as $I = \Delta V / R$. Power is $P = I\,\Delta V$. Capacitance is $C = Q/\Delta V$. The link to the field is $\lvert \vec E \rvert = \lvert \Delta V / \Delta r \rvert$ on the AP Physics 2 sheet, and $\Delta V = -\int \vec E \cdot d\vec r$ on the C: E&M one. Not one of them takes a bare $V$.

Where the zero comes from. A single potential gets a value only once a reference is fixed, and both sheets fix it in the exam conventions box: the electric potential is zero at an infinite distance from an isolated point charge. Change that choice and every $V$ shifts while every $\Delta V$ stays put.

In circuits. EK 10.5.A.3.i notes that a potential difference may also arise from chemical processes that separate charge, as in a battery, which is the emf. A 9 V battery has a 9 V gap between its terminals, not a potential of 9 V.