To be conscious, one must be both awake and alert.
Patients who sustain severe anoxic cortical damage, with brainstem sparing, exhibit wakefulness and sleep, but are not aware, and thus, are unconscious.
This description is the hallmark of a "vegetative state."
A coma is a deep depression in the state of altered level of consciousness, which is characterized by the patient's response to verbal or painful stimuli.