Anything you do stylishly is done fashionably or with elegance. Get your hair stylishly cut and all your friends will give you compliments!
You can obviously dress stylishly, in the latest fashions, or stylishly decorate your room, coordinating the wall paint with the colors of your bedspread and desk chair. But anything that can be done with graceful skill and confidence can also be done stylishly, so you can also publish a stylishly written memoir or stylishly execute another perfect strike in a bowling tournament.