The potential difference (also called electrical potential or electromotive force) in physics is measured in volts and is defined as an electric potential or electrical pressure between two points, especially two points in an electric circuit. So, in electrical engineering a potential difference means the same term as as "voltage".
The symbol for potential difference (voltage) is either "V" or "E".
In the SI system of units, potential difference is measured in volts, leading to the commonly used term voltage and the symbol V. Named after Alessandro Volta, one volt is defined to be one joule of energy per coulomb of charge. Count Alessandro Giuseppe Antonio Anastasio Volta (Como 18 February 1745 – Como 5 March 1827) was an Italian physicist known especially for the development of the first electric cell in 1800.
The potential difference between two points a and b is the line integral of the electric field E (derived from abbreviation of "electromotive force (emf)". The term electromotive force is due to Alessandro Volta (1745–1827), who invented the battery, or voltaic pile. "Electromotive force" originally referred to the 'force' with which positive and negative charges could be separated (that is, moved, hence "electromotive"), and was also called "electromotive power" (although it is not a power in the modern sense). Maxwell's 1865 explanation of what are now called Maxwell's equations used the term "electromotive force" for what is now called the electric field strength. Therefore in electrical engineering a potential difference means that the same term as "tension."
In mathematics, voltages can have a direct relationship (positive) or indirect relationship (negative) on what is being measured across two points (a,b). In fact, the differences in potential voltages across two points is called potential voltage. For example; Suppose we have a 5 VDC battery and a multimeter connected across two points (a, b) on our switch. Currently on a side our switch is in the OFF position so the switch contacts are open and there is a difference (minus, subtraction) of potential between the two meter leads, that results in a potential difference on the meter as 5 VDC (total applied voltage).
Next, when we move our switch to the ON position the voltage or potential pressure is “now” passing through the switch (contacts are closed), therefore the voltage is equal across two points or meter leads (a, b) on our switch that results in a potential difference (voltage) on the meter as ) 0VDC (no difference in potential)