The idea you wrote about emf and voltage is not actually correct.But the potential difference you defined is right.
Electromotive force, abbreviated emf (denoted and measured in volts), is the electrical intensity or "pressure" developed by a source of electrical energy such as a battery or generator.
Voltage, electric potential difference, electric pressure or electric tension (formally denoted ∆V or ∆U, but more often simply as V or U, for instance in the context of Ohm's or Kirchhoff's circuit laws) is the difference in electric potential between two points.