That's not a simple question and there isn't a simple answer. First, forget everything you've seen on TV or in movies. Those are fantasies. They have nothing to do with real life.
Partly it depends on what you're shot with, both firearm and ammunition. A rifle or shotgun will usually do far more damage than a handgun. Hollow point bullets will do more damage that simpler rounds. Ask an emergency room doctor about handgun wounds and they'll tell you stories for hours. Ask them about shotgun wounds and they'll go silent. Most shotgun victims go to the morgue, not the emergency room.
There's almost nowhere in the chest area you can be shot without damaging some organ or major blood vessel. Your lungs take up most of the space, along with your heart, major blood vessels, esophagus, trachea and diaphragm. Shoulders aren't much better. A shot there can destroy the brachial nerve complex, which will cripple the arm on that side, not to mention shattering bones in the area and bleeding into the chest. We haven't even talked about shock, yet, or infection and the consequences of that.
A hit on an arm or leg is apt to be less damaging, but, again, it depends. I know of cases where someone shot in the leg with a handgun FMJ practice round, went to the ER, effectively had a bandaid put on the wounds, and returned to the range to complete the class they were taking. There are endless tales of criminals shot in the act who ran away and drove themselves to the ER for treatment. On the other hand, I also know of a case where a criminal shot in the leg with a .45 ACP handgun hollow point round ended up having the leg amputated -- there wasn't enough muscle left to save it. Again, rifles and shotguns do much more damage.
Healing time is another issue and beyond my expertise. I suggest you ask a doctor or nurse about that.