If there is a "third world," what are the first two?

At one time, the “first world” meant the US and its allies [particularly in Europe], the “second world” meant the USSR and its allies, and the “third world” meant the non-aligned nations the first two worlds wanted to align with themselves. Since the fall of the USSR, “first world” has come to mean “highly industrialized nations” and “third world” means “under-developed countries.” What is “under-developed”? Does that mean they don’t have nuclear power? Or that they are not highly industrialized? And what of the vanished “second world”? Where does China fit in? Ir India? Or Thailand? Can the “second world” still be classified as non-democratic? As non-allied to the “West”? Aren’t Japan and Australia allied with the “West”? And maybe India? Inquiring minds want to know.