What's the difference between the Classic Wrap and the Half Beanie?

It's hard to see in some of the model pictures, so here is a shot of a Half Beanie and a Classic side by side. While the length is the same, the Half Beanie is much wider with a larger stitch (due to the thicker yarn used). The Classic has thinner ends making it easier to wear both over your hair and under your hair in a headband fashion.

What's the difference between a button back and a stitched back?

You can choose to have a button back or a stitched back. If you have longer hair and want it pulled up a button back is nice so you can wrap it around without messing up your hair. The stitched back sometimes gives a snugger fit and no need for a button - just slide it on. (pictured below) Unless requested otherwise, the Fuzzy Headwrap is always made with a stitched back. The reason is simply for ease.