Small addition to rob_g's commentary. In Canada you need two licenses to hunt. First is the license to have a firearm (PAL) and second is the hunting license. The hunting license is a provincial thing, the PAL is federal. Depending on exactly what you are going to hunt, you may also need a permit to kill that specific animal. Those regulations are specific to the province. For example, hunting squirrels you do not need a permit for. But for deer, pretty much anywhere in Canada, unless you are indigenous, you'll need a permit. I have a saltwater fishing license that lets me catch 4 crabs a day (8 when my son comes with me). But if I wanted to catch big fish in the ocean I'd usually need a permit specific to that fish.
The only hunting my grandparents would do is if a deer, moose or bear walked by their front door. Most people have to go a little further than that.
Whether or not you can hunt with an airgun is a provincially controlled thing. But generally speaking, yes with certain airguns you can hunt. You have to check the local regulations. Similarly, you are not allowed to hunt with handguns anywhere in Canada. Handguns have a different kind of license (restricted firearm) and can only be discharged at firing ranges.