A real pet is one where it i used for human companionship like dog, cat or gerbil. These have some kind need that the human can fulfil in the form of feeding and making a suitable habitat for that animal to live in. For children, the cyber pets that are available like Tamagotchi and Moshi Monsters also use human interaction to fill that void. I am yet to come accross one that is wild and can autonomously feed itself or keep itself happy.
The game of life invented by John Conway in 1970 is one that can, in a very simplified way, automate. This, if you don't know, is a set of algorithms that allows sprites to cluster and thrive or separate and die. The idea is that the randomness of the patterns is considered 'Wild'. Tamagotchi on the other hand are not wild. They are pre-programmed to 'need' from the inputs of the human. If the human denies the input then the Tamagotchi or Mimitchi goes into a comatose state that only allows feeding. The opposite to a dog or cat where, respectively, the dog dies (loyal and stays put) and the cat finds a place to live next door.
There is a grey area though. This is where the owner tries to tame a species of animal that really can't be tamed. We've seen them in all the extremes from iguanas to hyenas. This is where the wildness card is played and someone loses an appendage or two.
I've yet to hear of a Furby tear a chunk from the owner!