They do the the same thing, but do not mean the same thing.
The only reason that they do the same thing is the mere fact that an element id can only be used once in a page. If you take the same example, and use a different selector:
They will not do the same thing if there is more than one element with class some-class.
The first statement will apply to all the elements, the second will only apply to the first.
The second statement, by the way, would be considered poor practice. When using jQuery, use jQuery.
The  in the second statement takes advantage of the fact the the jQuery wrapped set created by the $() function acts like an array, and so  will fetch the first element from the wrapped set if one exists.
It's better to use the .get() wrapper method to fetch an item from the wrapped set.