Chemically there is no difference, hair and fur are from the same chemical ingredient called keratin. The only difference is how we people have learned to use the two words; we call it ’hair’ if it is growing on us and on animals that do not have dense follicles, such as pigs and elephants. We usually call the dense hair that grows on animals such as bears, lions and tigers ’fur’. As our cats and dogs have similarly dense hair, it is commonly referred to as ’fur’. However, lately the fur of companion animals has been called ’coat’ as another term, perhaps in order to underline their role in our life.