Horsepower terms used in pumps and pumping systems are:
Hydraulic horsepower - the energy required to pump a liquid if a pump were an ideal machine, i..e., there is no efficiency loss in the pump.
Water horsepower - the energy required to pump water.
Brake horsepower - the energy required to pump any liquid, except viscous liquids that require viscous correction in pump performance (see viscous horsepower.)
Viscous horsepower - the energy required to pump a viscous liquid where viscous correction in pump performance is required
Gas horsepower -
Horsepower recovery (horsepower recovered) - the energy recovered by a reverse-running pump acting as hydraulic power recovery turbine (HPRT).