For at least the present epoch, the world has been divided into four Elemental Nations: The Fire Nation (烈火國), Water Nation (洪流國), Air Nation (氣旋國), and Earth Nation (土強國). This situation prevailed from prehistory down until the Fire Nation's destruction of the Air Nation in 0 AG. The concept of an elemental nation is distinct from the government(s) that control them, and the Nations are not necessarily unified polities. For example the Water Nation is divided into the Northern (北方水族) and Southern tribes (南方水族), which share cultural links but are autonomous. Likewise, the now-defunct Air Nation was divided into the administrations of four Air Temples - the Southern Lama was primus inter pares among the leaders of the Air Nation theocracy, but his administration exercised no hard power over the other parts of the Air Nation. Before the Fire Nation conquests, the Earth Kingdom (土王國) represented the entire Earth Nation, but its control over its constituent polities is often theoretical and the Earth Nation is known for undergoing long cycles of division and reunification. On the other hand, the state controlling the Fire Nation also calls itself the Fire Nation, for obvious political reasons.
The type of bending a person with the potential to be a bender develops reflects the elemental nationality of their biological ancestors. People of mixed ethnic descent could develop bending from any of their ancestors' nationalities, with the odds being roughly proportional to their ethnic composition. Generally, people can have only one type of elemental bending, with a notable exception being the Avatar. It is not the case that people develop a type of bending based on where they live or are born: for example, the Foggy Swamp Tribe have lived in the Earth Kingdom since high antiquity, but they are waterbenders. They are, politically, Earth Nationals, but are ethnic Water Nationals and so develop waterbending.