Why does this AC axial cooling fan have 3 wires?
Yellow and Red are live and neutral connections to the run winding on the motor.

The green wire carries the AC voltage phase shifted by the capacitor, to the start winding. This is necessary to define the direction of rotation, to blow instead of suck.

Unlike a big single phase AC motor, the start winding is permanently connected, which is why the cap is an oil filled run capacitor, rather than a short term rated start capacitor (which would be disconnected by a centrifugal switch when the motor got up to speed)

And both windings will be a few ohms; measure on the motor side of the capacitor to see the other winding.