Hi Aladdin,

In the context of visualforce, to take advantage of the built-in features of Visualforce to access your org's data, you must use a controller. All controllers are Apex classes, either standard Apex classes (ApexPages.StandardController or ApexPages.StandardSetController) or your own custom Apex class. You can also extend the functionality of any of these with an Extension class.

I tend to be a bit picky with my terminology here. Controllers are controllers. Extensions are not controllers. And for me, the difference is that extensions cannot live by themselves on a page. In other words, I'm not permitted to use extensions, unless my page has a controller in the first place.

Another distinguishing feature is that a page is allowed only one controller ever. But I can add as many extensions as I need.

So let me begin (what has become a dissertation) with controllers:

Controllers are attached to your page using one of three mutually exclusive formats, a standard controller, standard list/set controller, custom controller.

For more detail Please refer to this link:
https://salesforce.stackexchange.com/questions/4041/difference-between-controller-and-extensions/4055

I hope you find the above solution helpful. If it does, please mark as Best Answer to help others too.
Thanks.
Deepali Kulshrestha