What is the difference? (Flash, Flex, and AIR, oh my!)

For several months, I was under the impression that the only way to make games and apps that compile into the SWF format was using Flash CS3/CS4.

However, recently, I have heard from various places about Adobe AIR, Flex, and Flash Develop.

What is the difference between all of these?
What formats does each one support?
How much do they cost?

Also, what is the difference between the AIR SDK or Flash SDK and regular AIR and Flash?