The goal of a hunter—I have hunted in the past, and I'm generally familiar with the culture—is a one-shot kill. That is what they strive to do. They are not interested in peppering the game animal with lots of holes. In the case of your moose or your deer, the ideal would be one shot.
Now, that doesn't always occur. A hunter may be shooting at a running animal and require follow-up shots. There may be something that happens at the time when the hunter is shooting and the bullet does not strike the animal in the desired location, and a follow-up shot is required. It's not infeasible to suggest that one or maybe two follow-up shots would be appropriate for big game hunting. I would say that most hunters would probably agree that emptying a mag of 20 shots, if it were available to hunters, is probably not what they want to do.
In the case of hunting birds, the regulations are very clear that, for hunting ducks and geese, which is regulated by the federal Migratory Birds Convention Act, hunters are permitted three cartridges. That's it. When a flock flies over, the hunter has three attempts to bring down three ducks or three geese or as many as they can with the allotted three shots. Then they must stop and reload.
For other game animals where a shotgun cartridge is used, the maximum number of cartridges will depend on the provincial hunting regulations. Typically that's somewhere around five, but that may vary from one province to the next.