You are correct. To create the potential difference the wire OR the magnetic field has to move perpendicular away or towards the wire this creates an induced current. But you cannot create the EMF without an external force. Be it from steam moving a turbine or electricity from a battery. In other words no matter what if I put in 24kW of energy in from the force, I better get 24kW of energy out or most of it out or accounted for. Either way electricity and magnetism are always together and part of the same force.
Thinking is not correct.