document.getElementById returns a DOM object. This is the browser's native way of thinking about an element in the page. It has various methods and properties. These can be a little clunky to use.
The jQuery object (created by the
$ method) is a wrapper around a DOM element or a set of DOM elements. The normal properties and methods are not available; you get a selection of different methods that make the process of DOM manipulation more intuitive.
The difference is more clear to see with multiple elements in the selection (as you would get with a class selector
$('.someClass') for instance, but the methods on a jQuery selection are different to the ones on a native DOM element. They point to the same thing, but they are different ways of thinking about it and dealing with it.
As a final note, you can convert a jQuery selection into its native DOM element(s) with the
get method (edit: or the alternative array-like syntax). So
is exactly the same as
$('#theID').get(0) // or $('#theId')
Note, however, that you should use the first, as it has much better performance. Only use jQuery if you need the extra functionality it provides.