It's easy Pea...
Flash is a plugin. It runs from withing the browser IE, Firefox, Safari, Opera, etc... It also can be run standalone, via special exe program on Windows platform.
Although this is less common. Here are all the Flash versions: http://helpx.adobe.com/flash-player/kb/archived-flash-player-versions.html
AIR is a cross platform runtime, kind of like Java (build once run everywhere). But with AIR it's a bit more tricky. You have to compile your program to each target platform (Desktop, Andriod, BlackBerry, iOS) separately. It's not like with Java where you can indeed run your jar file on lot of platforms. AIR is essentially Flash "on steroids" as it mostly has the same API as Flash and builds on top of it. But AIR not in the pluging form, i.e. you don't need a web browser to run it from.
Here are the latest AIR runtime: http://get.adobe.com/air/
You will need AIR SDK to build AIR applications and it has to be overlayed on top of Flex SDK which you can find here:
Now Flex SDK is essentially a component framework. You will need a button in your application, or a Video component, right? So that is what Flex provides for you free of charge.
Obviously this sound simple but Flex is much more then that and here is your
Flex documentation: http://www.adobe.com/devnet/flex/documentation.html
So, Flex is a component framework which lets you build applications which target either Flash or AIR as executable runtime. For Flash it is called Web application and it runs from withing browser or standalone Flash player. For AIR it is called Desktop or Mobile project and it runs from withing AIR runtime which has to be installed on your device or bundled with your application.
Now, speaking of Steve rants, yes, they wanted to kill Flash on their platform, there was even a guy there who was responsible for that result (I forgot his name but you can google), although Adobe never admited that and played it nice with Apple. Why they wanted to kill most expressive and complete vector and video engine on the web (Flash)? It's simple! This is beacase they wanted to play on their nice and cozy iOS/iPad/iPod playground alone! Because they want to control the delivery of the content from publisher to consumer. they want to stick their proprietory products and specifications in between and skim the money! That is why they don't need Flash in the browser. Flash allows people to publish and consume an impressive content without charging a dime! That includes H264 video among other things. And that is what Apple doesn't want to see.
Good luck with Flex and everything else,