The woman in white is a ghost who clings to this world, haunting men who are unfaithful to their wives/lovers. The individual ghost is the remnant of a woman who kills herself from a tragic lost love (Madam Butterfly style). She is usually extremely violent and causes direct harm to men.
The Woman in Black:
The woman in Black is a ghost who haunts the care-givers of children who are not the birth parents. She longs to be reunited with her own child, who was taken/lost, resulting in her killing herself. Usually much more manipulative than a woman in white, causing the care-givers to quarrel and ultimately trying to separate them so that she can take the child.
Conclusion: Bitches be crazy.
