Alright, I\'m confused by all the buzzwords and press release bingo going on.
The best answer I've found for "What is Flex" is at this page: http://www.adobe.com/products/flex/faq.html#flex-flash
Search for "How is Flex different from Flash?"
My interpretation of this is that if your application was generated from Flash Professional, it is a "Flash" application. If it was generated with the Flex SDK (Flash Builder, Flash Develop, or straight code & command line tools) it is a "Flex" application. Both "Flash" applications and "Flex" applications compile into bytecode that can be run by the "Flash Player" or by "Adobe AIR". Both types of applications can include "Actionscript" code.