EMF stands for the electromotive force and typically means the source voltage of the circuit, while the term voltage, while can mean the emf, is more general and can be applied to the voltage drop between different points of the circuit.
As previously stated, EMF stands for electromotive force. It is what makes the electrons move from atom to atom. How much electromotive force is present between two points in a circuit is measured in units of Volts. Voltage is a "Unit of Measure" .
If you were to apply enough electromotive force to move 3.25*10^18 electrons through a resistance of 1 ohm in one second, your voltmeter would read 1 volt.
Electrons being forced from their orbits around the nucleus of an atom by a source of electromotive force is called current flow. The unit of measure for current flow is the Ampere.
The tendency of electrons to remain in their orbit around the nucleus of an atom is called resistance.
Resistance is measured in units called Ohms.
Substances that allow their electrons to be forced from their orbits relatively easily are called conductors and generally we say their resistance is low.
Substances that do not easily allow their electrons to be forced from their orbits are generally referred to as insulators and we say that their resistance is high.
This is getting a off-topic but subtech's answer can be misleading. I'd like to prevent misunderstanding by someone trying to learn electronics note that the energies of electrons available for conduction in a solid are not limited to those of discrete atoms. The electrons used in conduction are not bound to orbits around individual electrons. Rather they exist in a "sea of electrons" within a band of energies. The location of these bands with respect to the fermi level and the temperature are what determine the resistance of a substance. http://hyperphysics.phy-astr.gsu.edu/Hbase/solids/band.html#c1
From a practical point of view you are most likely to come across the concept of EMF when dealing with batteries.
The reason is that the EMF of a battery is constant (depends on the chemistry) but the voltage across its terminals is not.
If the use the symbol E for EMF we can write
Where U is the voltage across the terminals of the battery, Ri the internal resistance of the battery and I the amount of current we are drawing from the battery. This (approximate) formula basically tells us that whenever we hook up a battery to a load the voltage drops.
This relation is useful because it allows us to predict what the voltage will be at a given load; you can find the value of the internal resistance in the data sheet of the battery.
This is something I did not know which in hindsight makes perfect sense when I think back to my physics texts.
"The emf represents energy per unit charge (voltage) which has been made available by the generating mechanism and is not a "force". The term emf is retained for historical reasons. It is useful to distinguish voltages which are generated from the voltage changes which occur in a circuit as a result of energy dissipation, e.g., in a resistor."