What are the different types of controllers use in a visualforce page
There are three types:
1) Standard Controller – Let’s you access the standard functions (Save, Edit, Delete etc) of a standard or custom object.
2) Custom Controller –  Let’s you add custom functionality by specifying an apex class that can define new functions for user actions (button clicks, link clicks etc).
3) Controller Extensions – Is a combination of Standard and Custom controllers.
Note:
You can have either a Standard or a Custom controller, but you cannot have both at the same time Controller Extensions can have more than one Apex Class.