Yes, $($(this)) is the same as $(this), the jQuery() or $() function is wonderfully idempotent. There is no reason for that particular construction (double wrapping of this), however, something I use as a shortcut for grabbing the first element only from a group, which involves similar double wrapping, is
$($('selector')[0])
Which amounts to, grab every element that matches selector, (which returns a jQuery object), then use [0] to grab the first one on the list (which returns a DOM object), then wrap it in $() again to turn it back into a jQuery object, which this time only contains a single element instead of a collection. It is roughly equivalent to
document.querySelectorAll('selector')[0];, which is pretty much
document.querySelector('selector');