There is the pressure shut off switch that is set to stop the motor once a predetermined pressure is reached. It would be wired directly to the motor. There is a pressure relief valve, also known as a pop off valve, that vents pressure should the pressure shut off switch fail to stop the motor from over pressurizing the tank. This is a spring loaded mechanical valve, usually brass, and is mounted on top of the tank. Then you have a regulator. It is usually plumbed into the pressurized air outlet on the tank. This regulator is where you set pressure to the line(s) supplying tools that are air powered.
Pressure relief valve looks something like this.
The wiring should look something like this. Wire colors may not be the same.
This is a dual regulator set up and how I prefer to do it to protect tools from moister and internal corrosion.