Flash and AIR work just the same on Android as they do on the PC - similar technologies, but Flash plays in a browser and AIR apps are used like native applications. In other words, to use an AIR app, you'll typically install it from the Google Market, and put a shortcut to it on your homescreen, then launch it and use it like any other application. Whereas for flash content, you'll follow a link or a bookmark, and see the content embedded within a web page.
Anyway the capabilities of the two engines are similar (AIR does basically all that Flash does, and adds on some extra features suitable for applications), but the difference is in the way you access and use the content.