In layman terms:
- Potential energy $U$: A term for "how strongly" a charge wants to move if it could. Put a negative charge close to the negative battery terminal, and it is repelled strongly. The electrical potential energy stored in such setup is huge. At different points throughout a circuit, a charge would be "pulled/pushed in" differently, so different points correspond to different amounts of potential energy.
Potential energy is in general defined as the amount of work that can be done. When strongly repelled or attracted, a huge amount of work can be done on the charge (giving it a huge amount of kinetic energy). So, how far/fast it will move if released, gives an idea of the amount of potential energy stored.
Potential $V$: This is just potential energy per charge, $V=U/q$. It is easier to compare points in a circuit by how they would affect the same amount of charge; therefore this term has been invented.
Potential difference $\Delta V$: This is just the difference in potential between two points. As when placing a ball on a high shelf, the ball will not want to start rolling sideways. The gravitational potential energy is the same at other points on the same shelf. It will only roll to a place of lower gravitational potential energy. Only the difference matters.
Since only the difference matters, we never care about the actual value of potential $V$ at a point. In fact, we can't ever know the true value. We only care about the difference between the potential at that point and another point. When someone says that "there is a potential of 2 V at this point", then they are actually comparing it to something else, usually to ground (which is at 0 V).
- Voltage $\Delta V$: Another term for potential difference.
Often, the symbols are a bit mixed up here. Often $V$ is used for voltage and can be confused with potential. You just must be clear on the meaning of a symbol in a specific context.
- Electromotive force (EMF): Think of EMF as "supplied" voltage. There is a voltage across the terminals of a battery, because the battery generates this voltage. It "supplies" this voltage. EMF is another word invented for such "supplied" voltage. Voltage can also be "supplied" due to magnetic induction and in other ways. In all such cases, the term EMF might be used. But it means nothing new.
The word "force" in the EMF term is a bit misleading. It is not a force. It is a "supply" of energy. But since energy differences (voltages) directly reflect how and whereto charges want to move due to repulsions/attractions in the circuit, "supplied" energy is sometimes thought of as a "driving force" for the flow of charges.