the max. range for a shotgun on game is going to depend on the shot pattern density at differant yardages. differant chokes and shell loads are going to be the main limiting factors.
a shotgunner needs to test his patterns and loads at differant yardages to see how dense they are. if a shot pattern at forty yards is dense enough that there are no holes in it that the game animal you are after could survive, then 40 yards is an acceptable range. a full choke 12ga. gun with the right loads may even have a farther lethal range on the animals mentioned than 40 yards.
the distance the pattern is lethal is important to know but a hunter should always try to get close enough to be sure.
it is up to a shotgunner to know what his gun and ammo will do as much as a rifleman to know his trajectories and bullets.
luck!