They are made up of the same thing much like finger nails and horns, but yet refer to something different. All mammals have hair but when referring to an animal they have hair or fur. The difference being the pattern of growth. There is secondary hair which refers to the hair that helps to regulate body temperature, and repels water, and primary hair which is typically coarser and longer than secondary hair which acts as a barrier for insects, twigs etc. Animals that are referred to as having fur have both primary and secondary hair whereas animals that have hair have only one of these types of hair. ex) polar bears have fur , humans have hair.