Nomesora
Your understanding is not at all accurate.
Brain death is accepted as death in all 50 states (though a few allow for a religious exception) and is routinely used in declaring death.
Brain death refers to the lack of function of the brain stem. The brain stem controls certain biological functions including breathing . The heart functions independently of the brain, It has its own pacemaker. Thus a brain dead patient, by definition cannot breathe on his own. However he will have a normal heart beat.
Most poskim reject brain death as a definition of death, they hold as long as there is a heartbeat the patient is alive. A few accept brain death either because they view the brain as decapitated, or because if a person can’t breathe then they are dead (even if the heart is still beating).
There is some question as to what R’Moshe held. He wrote a few teshuvoas on the subject which sound like he supported brain death. There is one yeshiva that is more explicit, but some have scheduled the authenticity of this teshuva
His sons (R Dovid can be seen on YouTube supporting this) and son in law and grandchildren all say he held brain death is halachic death, but others disagree.