are eddy currents and back emf the same thing?
no. eddy currents are currents, back emf is voltage. however both run on pretty much the same concepts.
when a solid conductor is exposed to a changing magnetic field, or is in relative motion to a magnetic field, currents will be induced in the conductor (by faraday's law). these are called eddy currents. the direction of eddy currents can be determined by lenz's law, and are found to oppose the original change in flux that caused them.
similarly, in a motor there is an original emf provided by the voltage supply. according to faraday's law of induction, there will be an induced emf running along the motor. the direction of the induced emf can also be determined by lenz's law, and is found to oppose the original emf supply hence the term "back emf".