Patients who suffer brain death are not in coma. Patients in coma may or may not progress to brain death.
The brain is a very complex organ. It is the brain that controls not only an individual's thought process and voluntary movements, but it controls involuntary movements and other vital body functions. These functions include auditory, olfactory, visual and tactile senses, regulation of body temperature, blood pressure, respiration, and heart rate (although the heart can continue to beat without the brain in "autotonic response"). The brain also produces hormones to control individual organ function. A good example is the brain's production of anti-diuretic hormone (ADH). This hormone is produced to concentrate the urine in the kidneys, thus protecting against life-threatening dehydration.
Patients in coma may be in deep coma or may survive in what is termed a "vegetative state." The difference between these two groups is that a deep coma patient usually requires hospital care, while a patient in a vegetative state may be released to the family for home care. The individual in the vegetative state has a lot more lower-brain function, and a bit more upper brain-stem function, than a patient in deep coma.
In either case, the patient is considered legally alive. Patients who are in coma will have some neurological signs. The amount of brain activity is variable, and extensive clinical examinations are performed on these patients. The physician(s) observes the patient for any sign of electrical impulse leaving the brain as a result of an external stimulus. Patients in coma will have these signs; patients who suffer brain death will not.