Horsepower (hp) is just a unit used to measure power of engines. Power = Work / Time. If we believe James Watt, 1hp is power needed to lift 550 pounds one foot in 1 second. So 1hp = 550 pounds x 1 foot / 1 sec.
Watts (w) is a unit used to measure power (joules per second). 1000w (1kw) is equal to 1.36 hp in the metric system which is often used.
Power on engine's crankshaft is bigger than power on wheels because pure power of engine's output has some loses in gearbox, differential, water pump, muffled exhaust system and other auxiliary components of an engine.
Brake horsepowers (bhp) is power on engine's crankshaft with no loses on other engine components. Brake refers to a device that holds engine's rpms to hold at desired value.
Wheel horsepowers (whp) is a effective and true measure for real power output because it's measured directly on wheels with all the loses in gearbox and other components. It's a measure of horsepowers that come directly on the wheels and ground. It measures on a dyno.
What's the number difference between whp and bhp? It's different in every car, some of them have more loses of power and some of them less. But usually we add 10-20% of power to get brake horsepowers from wheel horsepowers.
Nissan Skyline GT-R33 on a dyno:
picture by unigroup.com
