An electromagnetic field is induced by voltage (from a battery) running though a coil of electrically conductive wire. Basically this is describing a solenoid.
An eddy current is induced by a permanent magnet passing near an electrically conductive plate. You can feel the resistance of the magnet passing near the plate as the induced eddy current tries to slow down the speed of the magnet.
There is no such thing as "electromagnetic current".
electromagnetic current -- current is generated through the copper coil.
eddy current ---- current is generated through the iron core.
