Emf is the "potential difference (PD) across the terminals of a battery when it is giving no current to the circuit."
What does "when it is giving no current mean"? Will the PD across the terminals of battery when it is not giving current to the circuit equal to the case when the battery is giving current to the circuit?
If the internal resistance is coming into play to answer this question then I want to ask that "Internal resistance is present is present in both the cases, either the battery is giving no current or giving it to the circuit, then why do we not call the PD across battery terminals "emf" when it is giving current."
Best Answer
It's hard to sure without the context, but I'd guess that the definition is given that way because all batteries have a non-zero internal resistance, $R_i$, so if a current $I$ is flowing the measured voltage is $E - IR_i$ where $E$ is the EMF of the battery. The measured voltage only equals $E$ when $I$ is zero i.e. no current is flowing.