Calling jQuery plugin methods
Any performance difference would be too small to measure.

Code 2 pollutes the global namespace with three variables: $, fitvidsInit, and sliderInit.  Therefore, Code 1 is better.  I suggest eliminating $area and $slider as well:

jQuery( function( $ ) {

    // Responsive video
    $( "#sidebar" ).fitVids();

    // Image gallery
    $( ".owl-carousel" ).owlCarousel();

});