What is the difference between Flex and AIR application?

The “Flex Framework” is a collection of AS3 classes and components used in developing RIAs. “Flex Builder” is an IDE used to develop “Flex Applications.” If we use something other than Flex Builder to develop in Flex, we need to download the Flex SDK to compile. The end result of a compiled Flex Application is an SWF file (Same as Flash). With the compiled SWF file, a user only needs to have Flash Player installed to run the application. Most Flex apps are developed, deployed to a server and then a web browser is used to serve the application to the user for use.
AIR is an alternative delivery system for Flex Applications, replacing the web server and browser so to speak. It’s primary purpose is for deploying RIAs to a user’s desktop, independent of an internet connection. AIR, also allows for the use of HTML, AJAX etc. So an AIR Application could be a collection of all these things, compiled together. To run an AIR Application, we need AIR Runtime installed on our computer.