As long as your grill has a cover, you can cook on it with direct and indirect heat. In the case of direct heat, the food is positioned directly over a hot to moderately hot fire to sear and crisp its surface. Most of the world considers cooking food directly over an open fire to be the only form of grilling. Bistecca alla fiorentina in Tuscany, shrimp from the barby in Australia, and satay in Southeast Asia are all cooked in that manner.
With indirect grilling, the food is positioned away from the fire, and the grill cover is kept closed, reducing the cooking temperature and allowing the heat reflected from the cover to do the cooking. The indirect method is the only way to cook a turkey breast, pork roast, or other large cut of meat on a grill.
Considering everything cooked on a grill as “grilled” is akin to thinking that every dish prepared on a kitchen burner is “stoved,” regardless of whether you’ve deep-fried, sautéed, or boiled. Indirect cooking on a grill is really a form of oven roasting, a perfectly fine method of cooking, but one that yields neither the flavor nor the texture that’s characteristic of direct grilling. That’s why all of the recipes use direct heat. Also, for best results, keep the cover open for these recipes—unless, of course, you’re grilling in rainy or windy weather.