Simply put, neurofeedback is biofeedback for the brain. The only exception, however, is where more traditional forms of biofeedback are used to teach people skills that may only be used in specific situations (i.e.learning to decrease autonomic arousal during a panic attack); the goal of EEG biofeedback is actually to retrain the brain.
Note: Neurofeedback is also known as Brainwave, EEG Biofeedback, Neurotherapy, or Neuro