You cannot recover from brain death. If you’re brain-dead, you’re dead. There is no gray area (brain matter joke): either you are brain dead or you are not. If you are in a coma, on the other hand, you are legally very much alive. In a coma, you still have brain function, which doctors can measure by observing electrical activity and your reactions to external stimuli. In other words, your body continues to breathe, your heart beats, etc. Even better, you can, potentially, recover from a coma and regain consciousness.
