Difference between Custom Controller and Extension

Custom Controller:

• It is an Apex class that implements all of the logic for a page without leveraging a standard controller.
• You can use only one Apex class.
• You can Use custom controllers when you want your Visualforce page to run entirely in system mode, which does not enforce the permissions and field-level security of the current user.

Extension:

• A controller extension is any Apex class containing a constructor that takes a single argument of type ApexPages.
• It provides additional functionality to a controller – either a standard controller or a custom controller.
• You can use multiple Apex classes separated by comma.
• Use controller extensions when:You want to leverage the built-in functionality of a standard controller but override one or more actions, such as edit, view, save, or delete.You want to add new actions.You want to build a Visualforce page that respects user permissions. Although a controller extension class executes in system mode, if a controller extension extends a standard controller, the logic from the standard controller does not execute in system mode. Instead, it executes in user mode, in which permissions, field-level security, and sharing rules of the current user apply.

public class myControllerExtension {

    private final Account acct;
    
    // The extension constructor initializes the private member
    // variable acct by using the getRecord method from the standard
    // controller.
    public myControllerExtension(ApexPages.StandardController stdController) {
        this.acct = (Account)stdController.getRecord();
    }

    public String getGreeting() {
        return 'Hello ' + acct.name + ' (' + acct.id + ')';
    }
}

**********************************************************************************

<apex:page standardController="Account" extensions="myControllerExtension">
    {!greeting} <p/>
    <apex:form>
        <apex:inputField value="{!account.name}"/> <p/>
        <apex:commandButton value="Save" action="{!save}"/>
    </apex:form>
</apex:page>

**********************************************************************************

public class opportunityList2Con {
    // ApexPages.StandardSetController must be instantiated
    // for standard list controllers
    public ApexPages.StandardSetController setCon {
        get {
            if(setCon == null) {
                setCon = new ApexPages.StandardSetController(Database.getQueryLocator(
                    [SELECT Name, CloseDate FROM Opportunity]));
            }
            return setCon;
        }
        set;
    }

    // Initialize setCon and return a list of records
    public List<Opportunity> getOpportunities() {
        return (List<Opportunity>) setCon.getRecords();
    }
}

****************************************************************************************

<apex:page controller="opportunityList2Con">
    <apex:pageBlock>
        <apex:pageBlockTable value="{!opportunities}" var="o">
            <apex:column value="{!o.Name}"/>
            <apex:column value="{!o.CloseDate}"/>
        </apex:pageBlockTable>
    </apex:pageBlock>
</apex:page>

******************************************************************************************

public with sharing class AccountPagination {
    private final Account acct;  

    // The constructor passes in the standard controller defined
    // in the markup below
    public AccountPagination(ApexPages.StandardSetController controller) {
        this.acct = (Account)controller.getRecord(); 
    }    
    
    public ApexPages.StandardSetController accountRecords {
        get {
            if(accountRecords == null) {
                accountRecords = new ApexPages.StandardSetController(
                    Database.getQueryLocator([SELECT Name FROM Account WHERE Id NOT IN 
                        (SELECT AccountId FROM Opportunity WHERE IsClosed = true)]));
            }
            return accountRecords;
        }
        private set;
    }
    public List<Account> getAccountPagination() {
         return (List<Account>) accountRecords.getRecords();
    }  
}

******************************************************************************************

<apex:page standardController="Account" recordSetVar="accounts" extensions="AccountPagination">
    <apex:pageBlock title="Viewing Accounts">
        <apex:form id="theForm">
            <apex:pageBlockSection >
                <apex:dataList value="{!accountPagination}" var="acct" type="1">
                    {!acct.name}
                </apex:dataList>
            </apex:pageBlockSection>
            <apex:panelGrid columns="2">
                <apex:commandLink action="{!previous}">Previous</apex:commandlink>
                <apex:commandLink action="{!next}">Next</apex:commandlink>
            </apex:panelGrid>
        </apex:form> 
    </apex:pageBlock>
</apex:page>