The dog has decided that some aspect of the real doorbell is unique, and not shared with the TV bell. Another example of these dual behavioral principles occurs when you take your very obedient dog to a new location. The same dog who can sit, lie down, roll over, fetch and speak will become a distracted fool the instant he sets foot in a park. The dog has correctly discriminated that the park is different than your home, but has failed to generalize the commands associated with his obedience behaviors. The solution is to gradually introduce the dog to new locations, while continuing training on the behaviors that work at home.
Many dogs learn to dislike people who wear uniforms.
This reaction requires that the animal make both a subtle and complex discrimination AND a generalization. First the dog must learn to discriminate between people who wear uniforms, and people who do not. While we take for granted that uniforms differ from regular clothing, dogs must learn which components represent a uniform, and which things do not. This is not as easy as it seems. In reality, most uniforms are not really uniform.