The ingredients are usually the same, it's the amount of baking time that makes the difference. If you want chewy cookies, take them out of the oven when the centers look just a little bit underdone (let them sit on the cookie sheet a few minutes until they set up enough to move without tearing them) and then keep them in a covered container after they have cooled. Put wax paper in the container between the layers of cookies so they don't stick together.

The amount of moisture. Soft cookies have more moisture harder cookies have less moisture. Cooking time and temperature are the big difference. Baking for longer or at a higher temperature will cook out more moisture and create a harder cookie.

To make a chewy cookie you need to make a few changes to the ingredients list. I shouldn't say change you just modify the amount. Also a few small changes in the technique of mixing the cookie are needed. So here they are...

Ingredient Changes:

Reduce the number of egg whites. Egg whites in a bake good dry out the bake good that's actually part of their job.

Change the from white to brown sugar. Brown sugar not only has a little more moisture but the molasses helps hold on to more moisture in the cookie afterwards.

Next switch from AP flour to Bread flour. AP flour has a medium amount of protein in it where bread flour is high in protein. This protein is what forms more gluten in your cookie. Gluten is what makes doughs stretchy and in turn the cookie chewy.

Now when you make these changes do consider removing an egg white removes some moisture and you should add back a little. I do this by adding a little extra milk.

Technique Changes:

First instead of using your butter hard or even softened melt it completely. This actually breaks down the structure of the butter removing all "butter crystals" These crystals in a cookie would give it more structure and in the case of a chewy cookie we want less.

Most of the time you want to mix very little when bringing a cookie together because it will make it more crumbly and poofy. But in this case you want to mix it a little extra long. This will allow more gluten to form. I usually mix my chocolate chip cookies an extra 5 to 10 min on a medium speed before adding the chocolate chips for instance.

You will need to do is chill your cookies. After the melted butter and extra moisture you'll find that the batter you made is a little more liquid than normal. To keep the cookies from spreading and becoming very thin and then possibly drying out because they get burned you need to put them in the refrigerator until they are solid again. This take a good 30 min or so usually.

Good Luck!