The second example you show is a self executing anonymous function. Every separate JS file you use would probably benefit from using it. It provides a private scope where everything you declare with the var keyword remains inside that scope only:
(function($){
var special = "nice!";
})(jQuery);
alert(special); // would be undefined
The first example is shorthand for $(document).ready which fires when the DOM can be manipulated.
A couple cool things about it. First, you can use it inside the self executing function:
(function($){
$(function(){
// Run on DOM ready
});
// Run right away
})(jQuery);
Secondly, if all you need is a few lines in document ready, you can combine both the private scope and the DOM ready function like this:
jQuery(function($){
// $ = jQuery regardless of what it means
// outside this DOM ready function
});