The main difference between a Fowl and Chicken is that Fowl is a superorder of birdsand Chickens are domesticated fowls. Essentially, a chicken is a subcategory of fowls but not all fowls are chickens.
These two terms can be seen together in some cases, but they are two different things. Essentially, some Poultry can be considered Game, but Game encompasses more than just Poultry alone.
Aside from the competitive aspect of hunting and harvesting a buck deer, wild turkey, goose, etc. these animals are also some of the most nutritious meat