I'm pretty new at all thsi stuff too, and all these terms killed me for my first few weeks in this arena, but I've got my feet under me now.
Flex is an opensource SDK provided by Adobe (previously Macromedia). It used to be something they sold, but they opensourced it, Hoorah!!
Flash is the set of APIs that start with flash.*, and you can fully create flash animations with just the standard flash APIs.
Flex comes with a ton of very useful components, features, and functionalities that are built on top of flash. You should definitely download and get familiar with flex.
The flex api's start with mx.*
Flex also provides the ability to compile MXML documents into flash. MXML documents make it very easy to build Flash, full with animations, customizations, etc. in an HTML-like format. Take a look at the component explorer link below and you'll see the MXML generated for the example components. You can copy and paste that MXML (simple looking stuff eh?) and get a working app that you can expand on and play with as you learn.
Here are a few helpful links to get you moving in the right direction:
An interactive list of GUI components available in Flex (Flex isn't limited to just GUI components, but this is a nice place to whet your appetite):
A good list of Flex links:
The documentation available from Adobe is second to none:
Thats great news!!! Thank you so much!