document.getElementById returns a native DOM Element object, with direct access to that node's properties.
jQuery functions instead return "jQuery collections", i.e a jQuery object with an associated set of functions / plugins, etc that acts like an array of DOM nodes.
A common convention used to tell the former from the latter is to prefix variables containing the latter with $:
To extract the individual elements from a jQuery collection as DOM nodes, either use .get(n) or [n].
var $theList = $('#theList'); // jQuery collection
var theList = $theList[0]; // DOM node
var theList = $theList.get(0); // also a DOM node
Attribute and property access depends on whether you have a jQuery collection or not:
var id = $theList.attr('id'); // jQuery function
var id = theList.id; // native property