Q:

How does a hall effect wheel speed sensor work?

I have been researching how a wheel or crank speed sensor works in vehicles and am having a hard time finding a hard truth. 
I think I understand how it works simply. That the sensor detects a change in magnetic field and thus produces a hall voltage. The image below makes sense.
But internally what is going on? 
 
I have seen other images that show a magnet inside the sensor and thus producing a magnetic field. So when the metal rotor or crank comes close to the sensor is that magnetic field reduced or changed enough to then set off the sensor? Therefore, would producing a magnetic field at the end of the sensor produce a signal?

From "How To Mechatronics" Youtube Channel.
Ultimately, what is the magnetic field around the sensor doing that triggers the sensor? 

A:

But I was curious about how the magnet and the rotor interact to change the field to produce a signal.

This type of sensor is known as a "variable reluctance sensor".
Magnetic fields form loops, and you can think of the path that the field follows as a "magnetic circuit". The circuit includes a permanent magent (equivalent to a battery) and materials with varying amounts of reluctance (equivalent to resistance). Steel has low reluctance, while air has very high reluctance. The field intensity is equivalent to current.
In this case, the circuit includes the magnet, the gear, and the other steel structures that hold them relative to each other. As the toothed gear rotates, it periodically increases and reduces the air gap in the magnetic circuit, which directly decreases and increases, respectively, the field intensity passing through the Hall sensor.

