My understanding is that the second world referred to the communist nations, particularly the Soviet bloc. In this definition there is no second world any more (somehow China didn't count). Old world/new world refers to the world known to the ancients, where ancients is as defined by the Europeans. This would include Europe, Asia and Africa. The new world would then be the Americas. There is no congruence between the division of the world into old/new and the division into first/third.