The pump head of a centrifugal pump is more subtle than just the pressure difference that the pump produces. Most centrifugal pumps are driven by AC electric motors. Those motors produce a constant rpm (e.g, 1800 rpm or 3600 rpm) due to the frequency of the supply current and the construction details of the motor. Several physical phenomena occur as a result of this:
1) Since the pump is usually directly coupled to the motor, the pump impeller turns at the same rpm as the motor.
2) Motor horsepower requirements are determined by the flow rate through the pump AND the density of the pumped fluid. If a motor/pump combination is designed to pump something like gasoline and water is pumped instead, the higher density of the water will require that the motor draws more current in order to keep the pump impeller spinning at a constant rpm. In addition, for a constant impeller speed, the outlet pressure of the pumped fluid is directly related to the fluid density, with higher density fluids producing a higher outlet pressure.
3) For a constant impeller speed, the velocity of the liquid exiting the impeller is constant. This means that if the pump outlet was pointed directly up, with no attached piping, the liquid flow coming out of the pump would rise to a height that depends on its velocity exiting the pump. This height is known as the pump head.
4) The pump head is a function of the impeller speed, and it will be the same for all pumped fluids (in principle), while the pump discharge pressure will be a function of impeller speed AND fluid density. Thus, for the same pump head, different fluids will produce different pump discharge pressures and motor power requirements.
It is convenient to specify pump characteristics that will not vary with the pumped fluid, and pump head is one of those characteristics.