1st degree murder basically means any murder that was planned, 2nd degree murder means a homicide which took place at the same time as another felony, while 3rd degree murder refers to death that happens when the innovative intent was simply to harm the victim. Manslaughter is the crime of killing a person without hatred aforethought, or otherwise in situations not amounting to murder.
Anthony is pretty close. 1st degree means the murder was planned while 2nd degree means it was intentional but not premeditated. (What Anthony calls 2nd degree is really called felony murder). Manslaughter is death caused by extreme indifference to human life, like shooting into a crowd, where you don't intend to kill anyone but your act is extremely reckless.