What's the difference between
Nothing. People tend to use the $x syntax because it's easier to remember you're dealing with a jquery object rather than an element or an id.
In general I tend to use something similar to:
var $x = $(selector) //$x holds reference to a jquery object var elX = document.getElementById(id); // elX hold ref to an element node var xId = $(selector).attr('id'); //xId holds ref to an id attribute