@cinder- I can help break it down for you. All three of the terms you are asking about refer to work output, but they refer to power at different points in a Diesel or Otto (four-stroke gasoline) cycle engine. Brake horsepower, or bHP, is the power output of an unrestricted engine. This would be the output of an engine before a water pump, alternator, gearbox, differential, or exhaust are added, and it will be the highest published horsepower for a vehicle.
The horsepower at the wheels is the amount of power that is directly transferred to the roadway. The brake horsepower in cars and trucks can be much higher than the wheel horsepower in a vehicle. For example I have a pick-up truck that has 315 bHP with only about 271 HP at the wheels. The engine loses 44 HP from the engine to the wheels.