The difference between a pear-headed Chihuahua and an apple-headed Chihuahua is the shape of the skull. An apple-headed Chihuahua has a round, domed skull resembling an apple. The pear-headed, or deer, shape is flatter on top with a longer muzzle, resembling a pear more than an apple.
According to the American Chihuahua Breed Club's official standard, the correct look for a Chihuahua is always the "apple head." The head of the dog should be a domed round shape. Geneticists believe that the apple shape is a result of a combination of mutations causing brachycephalus and hydrocephalus. Brachycephaly is a malformation of the skull that causes it to be "squashed" in front, leading to a shortened muzzle. Hydrocephalus is an excessive amount of fluid around the brain, which can cause serious health problems. The deer shape appears to be somewhat brachycephalic, but is lacking the hydrocephalus-related dome. Pear-headed dogs suffer from fewer health problems and may be easier to obedience train, perhaps because they do not have hydrocephalus.
According to the American Chihuahua Breed Club, many Chihuahuas do suffer from health problems related to hydrocephalus. Symptoms of obstructive hydrocephalus include sleepiness, aggression, difficulty in housetraining, altered gait and, in extreme cases, seizures. However, if the Chihuahua has non-obstructive hydrocephalus there may be no apparent clinical signs.