The handle is viewed by the user as the actual class, but the work is done in the body. The Bridge pattern decouples an abstraction from its implementation, so that the two can vary independently. A household switch controlling lights, ceiling fans, etc. is an example of the Bridge. The purpose of the switch is to turn a device on or off. The actual switch can be implemented as a pull chain, simple two position switch, or a variety of dimmer switches.
Bridge is designed up-front to let the abstraction and the implementation vary independently.
Adapter is retrofitted to make unrelated classes work together. They differ in intent - that is, they solve different problems.