I have to way in here, as a quilting teacher, my answer is yes, it does need to be the same on both sides. It is easy to do. I usually use a 2 1/4" strips for binding and do the double fold method (this is the best method to use since it usually the binding that wears the most on any quilt) then machine sew it to the front of the quilt using a full quarter inch seam allowance and mitered corners, then trim backing and batting to equal a little less than half of your binding when it is folded out flat. Then, using the hidden running stitch hand sew the binding to the back of your quilt using the stitching line from the front as your guide to place your needle as close to the bottom side of the front stitching as possible. This is the way I do it, the way I teach it and the way several quilters I know who do show their quilts do it. Hope this helps. Good luck with your binding.
Hugs, Gail