This is a really confusing issue because the terms “Air” and “Jordan” mean something different from “Air Jordan”
An “Air Jordan” simply means one of the Michael Jordan signature shoes that have been released or reintroduced (retroed). These shoes will have a model number, which as of 2016 is between 1–30.
“Air” simply means a shoe that uses Nicke Air technology in the sole of the shoe, as all Air Jordans, and many other Nikes do.
“Jordan” simply refers to the Jordan brand, which markets “Air Jordans” as well as other footwear and apparel.
So, suppose the Jordan brand released a Chris Paul signature shoe that used Nike Air technology. It would be “Air” and it would be “Jordan” but it wouldn’t really be an “Air Jordan.”
Source:
https://www.quora.com/What-is-the-difference-between-Jordans-and-Nikes-Air-Jordans
https://www.sallyhouseoffashion.com/collections/sneakers/nike