What is Electromotive force (EMF)? How is it related to potential difference?
I dislike the term EMF (Electromotive force) as it is very confusing.
Electromotive force, also called emf (denoted $\mathcal{E}$ and measured in volts), is the voltage developed by any source of electrical energy such as a battery or dynamo.
Which means that all EMF are voltages but not all voltages are EMF. A voltage is only an EMF if it is a source of energy.
Kind of like the distinction between luminescent light (from a light bulb) and reflected light (from your desk) if you measure it there is no physical measurable difference. The only difference is that one is a source and the other is not.
Electromotive force, abbreviated as E.M.F and denoted by $\varepsilon$, is not a force. It is defined as the energy utilized in assembling a charge on the electrode of a battery when the circuit is open.Simply, it is the work done per unit charge which is the potential difference between the electrodes of the battery measured in volts. Mathematically, $\textbf{V} = \frac{\textbf{W}}{\textbf{q}}$.
Initially, energy is available in the form of chemical energy. This energy is utilized to take a charge say $+q$ to the anode by overcoming the electrostatic force of attraction due to the the negative charges on the cathode and the electrostatic force of repulsion due to the positive charges on the anode. The chemical energy then gets transformed into electrostatic potential energy present in the electric field between the electrodes of the battery.
The link you have provided answers pretty much all your answers, but still I'll quote and explain a bit more.
First The word "force" in this case is not used to mean mechanical force, measured in newtons, but a potential, or energy per unit of charge, measured in volts.
It is neither the creation of potential, nor it is a process and it is not even a force. It came to be known as a force because wrongful interpretation in the past made it seem as if a force from the battery pushed the particles in a circuit. This analysis was obviously discarded later but the name prevails!
In electric circuits emf and potential have a significant difference. While the emf is the potential difference between the terminals of a source in open circuit, the potential is the potential difference betwren the terminals in a closed one.
The potential is defined as $ V = \epsilon - Ir $. Here $\epsilon $ is the emf of the source and $ Ir $ is tue potential drop in the internal resistance. It is pretty clear that replacing potential with emf in any sort of circuit is not a very wise decision, however sometimes the potential drop in internal resistance is negligible.