Adobe Flash Player is a browser plug-in that provides advantages for users and content creators in the browser, including the ability to deliver RIAs in the browser. Adobe AIR incorporates technologies originally developed in Flash Player and enables rich Internet applications on the desktop. Adobe AIR and Flash Player provide complementary deployment methods for the RIAs.
as in here Here are a couple of conceptual questions :
Adobe AIR runs on the same technology as Flash (i.e. your AIR apps will run in the Flash player.) The difference is the additional libraries available in AIR to allow you to more easily create Rich Internet Applications, as opposed to Flash itself which is targeted at animation and games creation.
The end product of a compiled AIR application is either a .air file or a natively packaged .exe/.dmg file (if targeted at the desktop in AIR 2+)
The .air file is just a zip file which contains a .swf file and relevant directories from your project (such as unembedded assets).
The .exe file is the same except for it also contains code to download and install the Adobe AIR Runtime if the user does not have it installed on their system. This can be very useful if you want your application to run only on the desktop as it means users won't get an 'open this file with..' message when they run the app without the runtime installed.
The Adobe AIR runtime is what allows your operating system to interpret .air files and install/run them on the system. It contains the relevant AIR libraries not included in Flash.
Adobe AIR when combined with Flex (mxml application) does allow states and transitions. States and transitions are a feature of Flex, so you would need to be using the Flex SDK in your project to use them.