To me, the difference lies in decision making. There is very little decision making in archery (3D is a bit of an exception). But, what makes a great shooting bowhunter is the decision making prowess to decide when and how to shoot.
To complicate matters, bowhunting is a solitary sport and face-to-face learning is limited.
We have all heard same, old stories of the archers who can hit a bottle cap every time at 20 yards but can't double lung a deer at 15 while bowhunting. There is also the trite story of the guy who can't hit a pie plate at 20 but thinks he is deadly on game. Obviously, none of us think we are either of these guys but the harder question to answer is: What kind of bowhunter appears in the mirror?
This is the kind of self-reflection and examination that improves decision making and allows you to become a better game shot (IMO).