By helping your child identify the shared attributes of familiar objects (or furry friends), you're building key classification skills.
Years ago, developmental psychologists assumed that young children had very few skills when it came to classifying objects. While it is true that children have a more difficult time with class inclusion (ripe bananas are included in bananas which are included in fruits) children can classify many specific objects quite readily.
Children’s classification abilities are highly influenced by exposure. For instance, if you have a dog, your child may know much more about dogs (or at least your dog!) than a child without the same exposure to dogs. Your child might also be able to distinguish between a dog and a puppy.
Playing games that help children distinguish attributes of objects in their environment is great for development of these skills. For instance, playing a game to find all the pillows in the house helps children understand that all pillows have certain attributes (they are stuffed, have a covering, are soft) but may look different.