Why do we use fine wire of many turns in shunt field winding and thick wire of few turns in series field winding?

The size of the conductor (coil thickness) is related to the size of the current that can pass through it. We can see from the ampacity of this conductor.

And the number of turns is related to the inductance that is required to make the circuit works well. It depends on inductor function, is it for shunt winding, or series winding like in low pass filter circuit.