Direct grilling is the oldest method of cooking that involves direct exposure of food to fire. If you've ever roasted a marshmallow over a fire while camping, that's direct cooking. When direct cooking, the biggest variable is whether to keep the lid open or closed. Simply put, closing the lid keeps heat in, and lets your food cook more evenly on all sides.
Indirect grilling involves using the heat from a fire to cook the food but not putting it directly over the flames. This type of grilling is more similar to baking, relying on a convection effect where radiant heat cooks the food. Indirect grilling is a slower process allowing food to cook more evenly with less likelihood of burning areas exposed in direct grilling.
Smoking or "low and slow"
This is the process of slowly cooking tough meats with lower temperatures to get them tender and flavorful. Generally speaking, most meat smoking results are best when temperature is lower than in grilling.