I would suggest the following protocol that my farmer brothers observe;
1. Animals that you customarily give names to are not eaten; dogs, cats, horses, family pets.
2. Animals without names or identified by numbers are delicious; cows, goats, sheep, rabbits, any sort of fowl, etc...
3. If you give a name to any animal usually in category-2, then you can't eat it. Though you might sell it to someone else who will. This means if you plan to eat that cow or turkey, don't give it a "name".
4. Never lie to children about Rule-3, they'll never forgive you.
For Hunting the rules are simplier;
1. If it's "game" or fowl, then your obligated to eat it or give it to someone who will. The dogs and cats are family, so they can enjoy it for you. Some food-banks accept butchered game, check you state's game-laws first.
2. If it's varments (woodchucks typically), vermin or pests.... or game that you can hold within one-hand (ie. small game birds and fowl)....then it's best to re-cycle back into nature respectfully.