So far as I know, brake horsepower (BHP) and horsepower (HP) are the same. But some books tell me that the two concepts are totally different. What is the difference between BHP and HP?
For machinery that involves power transmission via shafts and gears, they are the same- and the actual term is brake (not "break") horsepower, because the apparatus used to measure the horsepower output of a machine is called a brake dynamometer.
For turbomachinery like jet engines where thrust is generated by movement of air, the concept of brake horsepower can't be applied- except in those cases where the turbine drives a propeller on a shaft. In these cases, the turbine's output shaft can be attached to a dynamometer and its horsepower output measured- and the result is quoted as shaft horsepower.
A horsepower is simply a measure of power, equivalent to 745 watts. The difference between types of horsepower measures in on a vehicle depend on if you include losses from the transmission.
For a turboprop or turboshaft engine, brake horsepower is the power at the output of the turbine, before any transmission. It is called brake horsepower after the brake dynamometer that is used to measure it. Essentially they are some form of brake that absorbs energy from a spinning shaft.
Shaft horsepower is the power delivered to the propeller or rotor shaft. That includes power losses from the transmission.
Equivalent shaft horsepower adds on additional thrust from the exhaust gases.
One more measure only applicable to cars is rear wheel horsepower. Measured at drive wheels, this includes power losses from the transfer (if applicable), differential, driveshafts, and tires.