Quite identical, yes.
They differ only in the places you refer to them. In the motors example, back emf is used as we are measuring the overall voltage across the entire coil, which does not form a closed loop in itself. We use this because the principal goal is to mesaure the resulting voltage, and we refer specifically to the voltage difference generated by the induced current.
(It could be argued that since the current generating the back emf forms a loop around the entire circuit and thus could be termed eddy current, but this is highly irrelevant to our intent.)
Eddy currents talk about the current itself as opposed to the voltage it 'generates'. This is often used when we are utilising some sort of magnetic field stuff, as the eddy current always proceed in a 'small' loop, generating a magnetic field.