There are 4 different styles embedded within bboying. They are Toprock, Bottomrock, Power Moves, and Freezes. Bboying isn't where you just pick one of these styles and use that, however. Bboying is really good when you find the perfect balance of all four in your dance. You want to use power moves to impress the crowd with your strength, freezes to impress them with your balance, toprock and bottomrock to impress them with your musicality. THat is how Bboying works.
In breakdancing, the music contains these breaks in the beat, and those and the end of the track are essentially where you would employ a freeze. For example, if the beat goes: (boom boom pow, boom ba boom pow, [pause] boom boom pow) the pause is where you would use a freeze. Sorry if that was a bad example.
Power moves are things that you would do while the beat is rolling. The reason they are called power moves is because they require much strength and force to execute. They can also require a lot of balance. Power moves are typically executed after some bottomrock or top rock. They usually work on any beat.
Top rock is a bboy style in which one is standing up and employing the use of footwork. The feet move, jump, flip, or other things. They are very on-beat. Basically, you're feet just follow the drums. Toprock can be used to transition between moves.
Bottom rock is a style of bboying that involves getting low to the ground and lots of intense footwork. It is much like toprock except it involves both hands and feet on the floor. Much of a person's body weight rests on their hands while their feet perform complex movements to the beat.