What is the difference between Deferred and Promise other than the jQuery versions?

What should I use for my need? I only want to call the fooExecute(). I only need the fooStart() and fooEnd() to toggle the html div status for example.

//I'm using jQuery v2.0.0
function fooStart() { /* Start Notification */ }
function fooEnd() { /* End Notification */ }
function fooExecute() { /* Execute the scripts */ }

$('#button1').on('click', function() {
    var deferred1 = $.Deferred();
    var promise1 = $.Promise();

    deferred1.???

    promise1.???
});