If you take a Magnet and move it relative to a Conductor, a current is made to flow in that conductor. The magnitude of that Current is dependent on many things, including the Magnetic Flux density cutting the wire; the relative Speed of the Magnet; the number of turns the conductor makes, etc. It can be said that the Moving Flux lines "cutting" the conductor's path induces an Electro Motive Force, an "E.M.F."

Conversely, if an electrical Current is passed through a Conductor, a Magnetic Field (Flux Lines) forms around the Conductor. With a sufficient number of turns of wire one has an Electro Magnet.

If one were to place two Conductors side by side; one passing a steady Electric Current; the other wire is unaffected. Although there are Magnetic Flux lines "cutting" the second Conductor, No E.M.F. is generated since there is No Relative Motion.
However, if the Electric Current is made to vary in Magnitude and/or Polarity, then there would be an Induction of an E.M.F into the second Conductor, i.e., this variation/change in Magnetic Flux has the same Effect as Relative Motion between the Magnetic source and the Conductor