Wrapper Class vs Helper Class vs Controller Class

Wrapper Class: To wrap the Data types to make a single object which can be assessable easily in other classes.

Controller Class Controller class contains public methods called Action methods. Each method has a one-to-one link with a possible user action, ranging from the click of a button to another trigger. The controller class methods process input data, execute application logic and determine view.

public class WrapNitesh {

//CONTROLLER CLASS

    public list<wrapaccount> wrapaccountList { get; set; }
    public list<account> selectedAccounts{get;set;}    

      public WrapNitesh (){

     //if(wrapaccountList ==null){
          wrapaccountList =new list<wrapaccount>();
          for(account a:[select id,name,billingcity,phone from account limit 10]){
           wrapaccountlist.add(new wrapaccount(a));

           }
        // }
      }

    //### SELECTED ACCOUNT SHOWN BY THIS METHOD
      public void ProcessSelected(){
     selectedAccounts=new list<account>();

      for(wrapaccount wrapobj:wrapaccountlist){
           if(wrapobj.isSelected==true){
           selectedAccounts.add(wrapobj.accn);
           }

         }
      }

  //##THIS IS WRAPPER CLASS
   // account and checkbox taken in wrapper class

   public class wrapaccount{

    public account accn{get;set;}
    public boolean isSelected{get;set;}

       public wrapaccount(account a){

         accn=a;
         isselected=false;
       }
  }
}

Helper Class helper class is used to assist in providing some functionality, which isn't the main goal of the application or class in which it is used

function linesOf($mls) {
    return preg_split('/\s*\n\s*/',trim($mls));
}