Brain dead is also known as brain stem death.
Brain death, or brain stem death, signifies the irreversible cessation of all brain functions, including the brain stem. This means the individual has no capacity for consciousness, awareness, thought, or voluntary movement, and cannot breathe independently. It's a state where the person is legally and medically confirmed as dead, even though their heart may still be beating thanks to artificial life support.
In summary, while both terms refer to the same condition, "brain stem death" emphasizes that the critical area controlling vital functions like breathing has permanently ceased to function.