If we are being picky, Really, both only have one field.

An electro magnetic field is like anything else elctrical. It needs power, and ground.

On the old ones, the power is regulated, and the ground is constant through the case of the alternator.

On the newer ones, the power is key on battery voltage, and the ground is regulated through the second wire.

Yes, grounding the second terminal completes the circuit when running a newer alt, with an older style reg.