To my mind, a bird (water bird or otherwise) must fly eihter high, or far, or frequent, to be called that. It must use its wings.
That's a very reasonable explanation, maahey. The same tends to apply to chickens and turkeys - not water-fowl but similarly reluctant to aviate. And also referred to as fowl.
(Mind you, when a swan does decide to fly, it is an awe-inspiring sight!)
As an aside, I think that "game-bird" is a term only applied to ones that rich people go out and shoot - e.g., pheasants and grouse - pampered beasts that are cossetted by game-keepers until the time for their slaughter arrives.
Wild ducks and geese also get shot at, but not exclusively by rich landowners and their guests (often paying guests, at that!) nor are wild-fowl reaered (fairly obviously, I s'pose.) Wild-fowling is a sport - over here at least - that can be followed by anyone licenced to carry a shotgun.
(there are local regulations and licences, of course.)
