In your everyday nuclear fission process a neutron bullet is fired at and captured by a heavy element atom like uranium. That extra energy from the neutron causes the heavy atom to split into at least two lighter elements.
But when that heavy one does split the total binding energy, called the strong nuclear force, of the two lighter elements is less than the binding energy of the one heavy one. And the difference between the heavy element binding energy and the two lighter ones is called the mass energy difference, which is that e = mc^2.
It’s called the mass energy difference because in fact the mass of the one heavy element is actually greater than the total mass of the two lighter atoms. So it’s the difference in the two binding energies, the strong nuclear forces, that is the conversion of mass into energy e = mc^2.