The Flex SDK is the bare minimum needed to develop a Flex
app: the compilers and the component libraries. With the SDK,
you'll have to use your own text editor and run the compiler
manually. It's awkward but at least it's free. I would not
recommend this approach (to anyone).
Flex Builder 2 is an IDE for developing Flex apps. Under the
hood, it uses the SDK, but most of the gory details are hidden from
you. It really streamlines the development process with visual
design tools, code completion, etc. It does cost money, but if
you're serious about Flex development, it's worth the cost. It has
a free 30-day trial, so take it for a spin.