What produces electricity by spinning a magnet in a coil of wire?

A generator or alternator.

If the magnetic field is permanent, the current produced from the coil will be alternating current. AC.

Alternators usually work the other way round. The magnet is spun inside a coil of wire. The power is taken off from the stator.

The rotor is an electromagnet, fed via slip rings on the shaft. The strength of the magnet can be varied and controlled externally, to control the output voltage.