death vs cerebral death

death and cerebral death both are nouns.

Word	Noun	Adjective	Verb	Adverb
death	Yes	No	No	No
cerebral death	Yes	No	No	No

As nouns, cerebral death is a hyponym of death; that is, cerebral death is a word with a more specific, narrower meaning than death:

death: the permanent end of all life functions in an organism or part of an organism
cerebral death: death when respiration and other reflexes are absent; consciousness is gone; organs can be removed for transplantation before the heartbeat stops

Other hyponyms of death include cell death, necrobiosis, gangrene, mortification, necrosis, sphacelus, brain death.

death (noun)	cerebral death (noun)
the act of killing	death when respiration and other reflexes are absent; consciousness is gone; organs can be removed for transplantation before the heartbeat stops
the event of dying or departure from life
the permanent end of all life functions in an organism or part of an organism
the absence of life or state of being dead
a final state
the time when something ends
the time at which life ends; continuing until dead