The chief difference between a camping grill and a camping stove is the way that the heat reaches, and therefore cooks, the food. With a camping grill, the flame is allowed to reach upward and freely come into contact with your food, be it burgers, hot dogs, or corn on the cob. This direct-fire method heats the grill plate which not only produces those aesthetically pleasing grill marks, but allows for precise control over how the food is being cooked.
A camping stove, on the other hand, features a small ring of flame that is designed to heat a pot with liquid in it. This is more ideal for meals like soup, oatmeal, cocoa, & coffee, where the main intention is to heat liquid efficiently. Because there is a barrier between the heating element and the food (the pot or pan), camping stoves are generally much easier to clean.