Flash Builder is in fact the latest version of Flex Builder. It is essentially Flex Builder 4.0 - Adobe changed the name.
Flex is the Framework - nothing more.
Your confusion is entirely understandable.
Thank you answer. now can you tell me what is difference between Flex and Flex builder.
Flex is a software framework with an SDK - it's essentially a library+markup language (MXML)+compiler.
Flex Builder is an IDE (Integrated Development Environment) for developing with Flex.
You can use Flex using the compiler, or buy the IDE (Flash Builder 4).