The short answer to your question is "not much".
Flash was a tool designed primarily for animation, so the major metaphor within Flash is what they call "the stage". Once developers wanted to use Flash for things that weren't quite animation ("animation" here means things like cartoons), the stage as a development metaphor didn't quite work. So, Adobe released Flex, which is effectively the same thing as Flash (both rely on ActionScript, both compile down to SWF files, etc), but in a more traditional development environment.
That's the biggest difference.