You have 4 pins. When you apply 12 VDC to the 12V pin and ground the fan runs at about 1350 RPM which is maximum speed. Your fan has 4 pins. In addition to 12 volt power you have a tach out normally two pulses per revolution and you have a PWM (Pulse Width Modulation) input. Try something. With the fan powered as you have running full speed try connecting the PWM in pin to ground rather than have it just float. Does the fan stop?
Should that work and you have a source of PWM pulses you can apply your PWM pulses to the PWM in pin. The tach out is strictly an output so a cpu can determine the fan speed. The PWM as was mentioned is simply turning the fan On/Off at a very fast rate. This makes for fan speed control. Likely as mentioned using a MOSFET internal to the fan. Figure at full speed the fan only draws 110 mA so a tiny little N Channel MOSFET is easily embedded in the fan case.
Ron