Voltage is an electromotive force created by a difference of potential. Therefore the terms voltage and difference of potential can be interchangeably used.
The term "difference of potential" is often used in describing the ability of an electric circuit to create movement. Just like in Physics you have potential energy and kinetic energy, in electricity you can describe the phenomena the same.
Electric current flows by making a circuit have a potential difference at the source. Then by connecting those two potentials with a conductor (wire), you're able to make a strong current of electrons flood through the conductor from the source, back to the source.
A battery has two different types of metal inside of it. One piece is made of a material that freely gives up electrons, and the other freely receives electrons. Just the ability for these two pieces of metal to have a relationship of proximity, is enough to capture and utilize the atomic energy they create.
Another good example is lightning. When the clouds fill up with positive charges, and the air closer to the ground has more negative charges a discharge of electric energy will occur. There is a difference of potential between the clouds and the ground, so current can flow. After a thunderstorm has passed the charges equalize and everything goes back to being the same potential.
You can think of electricity similarly as you'd think of water. Electricity flows and has a current, as does water. There's a pressure to that current depending on the voltage, or difference of potential, of the source...just as water uses the difference of potential created by gravity and height. Water flowing down a small slide will flow gently. Water flowing down Niagra Falls will kill you. Both the difference of potential as well as the current (or amount of flow) increases dramatically.
In order for electricity to work, there has to be movement. Static electricity still needs movement to occur in order to discharge and equalize charges. The only way that movement becomes useful is once there is a difference of potential present. That is what voltage is all about.
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**Disclaimer - These videos are for training purposes alone, all work done on electrical systems should be done by a licensed and insured electrical contractor. If you are not an electrician, do not attempt any of the work you are seeing in these videos.**