this refers to the current element while $(this) is the jQuery object which is constructed with that element . Using $(this) we can enable jquery functionalities while if we use this it has only generic javascript functionalities. When we need to access the basic javascript methods always use this while if you are using jquery use $(this). Sometime it is much quicker to use this instead of $(this). For example

$(".chkbox").change(function(){ 
    if(this.checked) 
       alert("checked"); 
});

$(".myCheckboxes").change(function(){ 
      if($(this).is(":checked")) 
         alert("checked"); 
});

this reference a javascript object while $(this) is used to encapsulate with jQuery

var name = $(this).attr('name');
$(this).css('background-color','red')

// Getting form object and its data and work on..
this = document.getElementsByName("newvar")[0]
formData = new FormData(this)

// Calling blur method on find input field with help of both as below
$(this).find('input[type=text]')[0].blur()

//Above is equivalent to
this = $(this).find('input[type=text]')[0]
this.blur()

//Find value of a text field with id "index-number"
this = document.getElementById("index-number");
this.value

or

this = $('#index-number');
$(this).val(); 
$(this).css('color','red')