Aj, full name of airjordan, is a brand specially established by Nike for Jordan. In the eyes of China people, there are two Jordans, one is a Jordan owned by Nike, and the other is a Jordan from Fujian, China. Jordan in China is a brand established by a dealer in China under the name of Jordan, with the logo of Jordan.
China consumers are used to calling it "Jordan" or "Air Jordan". It is a brand of Nike and belongs to Nike. For example, Nike is the United States, then AJ is like California or Texas, or North Carolina, and so on. And "Jordan" is a brand of sporting goods in China. Generally speaking, most people can refer to "AirJordan" when they say "Jordan". So it is not entirely correct to say that aj and Jordan are the same brand.