William's answer is good and I mostly agree with what he is saying, but undoubtedely there will be some overlap between questions about livestock and questions about pets.
A person not too far from my house keeps chickens technically as a pet, but in reality they are being kept for a single useful function and that is that they produce eggs. VERY delicious eggs I might add. The municipality I live in does not allow livestock to be kept on property zoned as residential, so legally these animals are kept as pets. The children however love their chickens, name them and feed them. The children feel a bond with the animals however the parents wouldn't shed a tear if one were to get sick. If one got too old to lay eggs it would likely be killed and made into a pot pie. To the parents their chickens are livestock.
So a pet then can have a variable legal definition depending on laws or ordinances in your area. It even gets blurry when you are talking about a dairy cow, "I'm gonna go milk Bessy..." Clearly it is livestock, however they named the cow. The act of naming the animal implies a relationship too.
So legally, and mentally and emotionally an animal can be both a pet and livestock. The questions will undoubtedly overlap too... "My horse has a growth on his one foot, is this something I should worry about?". The horse could be a beloved pet or valuable livestock or both.
However the kick is, if the question, "When a dog is excessively drinking water, what can this be a sign of?" doesn't imply ownership of a single animal or a relationship with an animal, then we can no longer assume that it is a concerned pet owner, and perhaps it is a first year veternary student looking to cheat on his homework.
Pets are owned by people and have some kind of relationship with the owners. A valid question about a pet should be anyone where ownership and relationship are established in the question.