Flex is absolutely Flash. It is simply a library/toolkit for Flash development.
Oh wait, you can't.
Seriously, they're not the same thing. Flex is a toolkit that compiles to swf but its not flash.
Flash, as something you hire developers for, is an authoring environment. As of CS3, it is not very compatable with Flex.
CS4 actually as adobe tying them together a lot better, but I've yet to put enough time in on CS4 projects to know one way or the other how well they have.
While you may think of flash as "that which runs on a flash player", a vast majority of people developing software in this arena think of it as "that which is written with the component of Adobe Creative Suite 3/4 called Flash Builder"