What is the difference between BHP (brake horsepower) and HP (horsepower)?
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.