Original: The four genera are the great albatrosses (Diomedea), the mollymawks (Thalassarche), the North Pacific albatrosses (Phoebastria), and the sooty albatrosses or sooties (Phoebetria). Of the four genera, the North Pacific albatrosses are considered to be a sister taxon to the great albatrosses, while the sooty albatrosses are considered closer to the mollymawks.
Simplified: There are four main species of albatross: Great Albatrosses, North Pacific Albatrosses, Mollymawks and Sooty Albatrosses.