Hi SKT,

StandardSetController is a class whose objects allow you to create list controllers similar to, or as extensions of, the pre-built Visualforce list controllers provided by Salesforce.

Below are details on standard controller and StandardSetController which explain the difference between 2.

StandardController
From documentation: A Visualforce controller is a set of instructions that specify what happens when a user interacts with the components specified in associated Visualforce markup, such as when a user clicks a button or link. Controllers also provide access to the data that should be displayed in a page, and can modify component behavior.
Basically, a StandardController is for ONE record, i.e. if you'd like to create a new Visualforce page for a single record, you'd use a Standard Controller in your Apex. For example:
public with sharing class MyController {
    private ApexPages.StandardController controller;
 
    public MyController(ApexPages.StandardController controller) {
        this.controller = controller;
    }  
    // maybe this gets called from a button within your VF page
    public void doSomethingWithSingleRecord() {
        SObject record = controller.getRecord();
 
        record.put('Status__c', true);
        update record;
    }
 
}
 
StandardSetController
From documentation: Standard list controllers allow you to create Visualforce pages that can display or act on a set of records. Examples of existing Salesforce pages that work with a set of records include list pages, related lists, and mass action pages.
Basically, Set (list) controllers are for MULTIPLE (or a list of) records, i.e. if you'd like to create a new Visualforce page for a List of records (or even from a selection of records on a List view), you'd use a Standard Set Controller in your Apex. For example:
public with sharing class MyController {
    private ApexPages.StandardSetController setController;
 
    public MyController(ApexPages.StandardSetController setController) {
        this.setController = controller;
    }
    //maybe this gets called from a button on your list view
    public void doSomethingWithMultipleRecords() {
        List<SObject> records = setController.getSelected();
 
        for(SObject record : records) {
            record.put('Status__c', true);
        }
 
        update records;
    }
}
 
Thanks,
Puneet