One interesting to note is that in general, animals used as food usually eat plants, while animals used as pets usually eat meat. This isn't always the case, of course, but chickens/cows/pigs are herbivores while dogs/cats are carnivores. So extra animals need to be eaten for both the humans, and their pets.
(of course, rabbits and birds can be pets but I think cats/dogs are most common)
As for the difference, I guess we just don't have to think about it too much. People choose what makes them feel good without thinking too much about it - meat is tasty (carnivores usually don't taste as good I guess) but pets are fluffy and cute if you're with them. Also, cows and pigs are harder to have as pets, anyway, I'm guessing...
Cows and horses are herbivorous pets. Many vegetarians and vegans raise their dogs vegetarian or vegan only. On the other hand, chickens and fishes are fed meat products in their feed.
Actually, all these choices are arbitrary and without any logic. People don't always make rational choices. They just blindly follow the tradition with the herd mentality. All that you mention may appear to be true because most of us look at things from a pre-occupied mindset. Otherwise, none of it is true. Carnivores' meat is not tasty and other meat is tasty type of facts are mentioned without actually comparing all food. There is no denying that plant-based food is most delicious and tasty in comparison to any food. Everyone finds their pets as cute irrespective of their breed. Many people keep cows and pigs as pets too. There is no problem in keeping them as pets. In fact pigs and cows are very intelligent creatures.