The Four Chinas are four distinct states that followed in the wake of the Collapse when the Communists in China fell. Theses consists of the Qi Empire, Ming Empire, the People's Republic of China, and the People's Directorate of China.
American Tibet was nuked into oblivion, and the Communist state was nuked in all its major cities sending it into complete civil conflict. The People's Liberation Army retreated into the lands in Western China where they still had surviving strongholds and founding the People's Directorate of China. The main surviving government fell, but was soon restored, bearing its same name. Both countries went to war, but ultimately made no headway against one another.
The Qi Empire was formed around the Yangze. With most of its cities destroyed it was originally agricultural, but it soon modernized in the decades after the Collapse and the invasion of the People's Liberation Army.
The Ming was formed by a few surviving members of the Zhu family which ruled over China before the Qing did. Gathering support in the wake of the Collapse they formed a rather peaceful empire. When conflicts came, however, it quickly devolved into a military dictatorship headed by an Emperor. Wars with the Celestial Empire of Siam and the People's Liberation army turned it into the second most totalitarian nation in the world. Together the Three Chinas formed a temporary alliance against the PLA, if the PLA should invade one of them, the other two would come to their aid. This has left China in a state of cold war.