Social construct.

[Jehanne]

Absolutely true in the case of cats, but, much less so in the case of dogs.  But if a cat owner would die in their home and not be noticed, the surviving cats will sometimes scavenge the remains of their now dead owners.  Once consumed the cats may be trapped in their owner's hone unable to escape and succumb to natural causes, likely, dehydration.

This is all believable about dogs and cats. But both animals kept as pets and animals in the wild die of natural causes if they get trapped in something. So I don't see any biological difference there.

Nothing so far works against the idea that the concept of "pet" is a social construct. Even if it's a construct made by scientists, it's not something you can determine by DNA analysis. 

Suppose a pair of animals are identical twins, or clones. You keep one as a pet, and the other lives feral outside. If the DNA is identical, then the pet-ness of one is a social construct. 

Likewise with weeds. One man's weed is another man's cash crop. What determines the weed-ness of a plant is desirability to gardeners, not DNA.

Dogs can be kept as pets; wolves, typically, cannot be kept as pets. This process is one of domestication of animals, which was a process over time of artificial selection. The fact that wolves have brains allowed some long ago to begin their long process of cohabitation with Homo sapiens -- wolves that were congenial were kept and allowed to breed while those that were not likely were set back into the wild or even killed. Thus began the slow process of artificial selection and the subsequent domestication of the dog.

Now, is marijuana a weed or a grass? This is the area of taxonomy, the classification of plants and animals. Such is a science and organisms, both living and dead, are classified based upon their evolutionary relationships, phenology, morphology, etc.