jQuery.noConflict()

jQuery is included in WordPress in noConflict mode, so as to work with other javascript extensions that also use $ as an alias.

Hence your above Version II will not work with the WP native jQuery loading.

What is jQuery?

jQuery is not a language. It is nothing but a (massive) javascript object. That object's name is jQuery. When .noConflict() is not applied, $ is an alias for the jQuery object.

Best practice for external files

Wrap the entire js in a closureclosure, pass it the jQuery object and $ as an argument. Inside you can write your script the way you're used to:

(function($){
    $(document).ready(function() {
        $("#radio").buttonset();
    }
})(jQuery);