http://theresidentalien.typepad.com/ginormous/2009/02/the-difference-between-flex-and-flash.html

this url will clear you the difference

Flash was basically designed for designing purpose. If you want to do animations , designing work like creating graphics etc you should use flash. Flash uses core actionscript which means the original classes of actionscript unlike flex which uses flex framework.

Flex is used to create applications with forms and data etc. Flex have many inbuild components and it have a set of classes which is called Flex framework. All the components use flex framework, which provides many ready to use classes and thus make the life of a flex developer very easy. Flex does not provide a timeline and you cannot draw anything in flex. If you want to use complex drawing objects then you have to draw them in flash and then use them in flex. Simple drawing like circle, rectangle, lines are possible in flex using scripting.

Flash is for designers and Flex for developers.

Let me know if you have any questions

Bob to some extent I disagree that flash is for designers. If you see Flex sometimes depend on Flash but Flash can handle all the things inside it, design + development. IF I am not wrong then in Flash if we choose file for as2.0 then in the components panel we see one data component but for as3.0 it is not there because it is in flex now. For promoting flex few things were taken from flash in as3.0 version. I would like to hear your views on this.

Actually in initial versions the flash was created for only animations, then eventually as it got popular actionscripting was improved. After actionscript 2.0 and Flash 7 release. Adobe noticed that now flash was widely being used to create online web applications and not just animations. Flash is base like C for flash but it was not friendly for developers.
For developers some major drawbacks in flash are:

Components are not strongly intergrated.
Difficult to work with big team.
Debugging was very difficult
Code hints poorly supported
Errors will show after compilation

So adobe created flex as development environment and flex framework which provides many additional classes to make development extremely fast and easy.

Flash is more powerful as compared to flex because it is based on basic classes, just like C (Flash) and C++ (Flex). Developers do not require timeline so flex provided just development features and interface. As you said flash can handle everything , that's true , but its not product which is designed for development. If you work with big projects then you will soon realize that its terrible to develop big applications in flash. Wide acceptance of flex is the proof of its need over flash.

As a developer you may only need to learn very small part of flash, like to create skins and components to use in flex.

If you are interested in development I will strongly recommend you to learn flex along with basic knowledge of flash. But if you are a designer then you can only learn flash with as3.

Thanks for replying in detail. I think this will clear any person what is the difference between flash and flex.

Thanks for replying.
It's really helpful.