The difference between mammalian hair and fur is chiefly one of arrangement, not structure. Hair tends to come individual strands that are fairly coarse, as well as being patchy in concentration.
In people, for example, there is little in the genital area and underarms and some on the male face and chest, plus a dusting of individual, visible separated hairs on the rest of the body.
Fur on the other hand, tends to coat the body of the animal in a closely packed arrangement, so that the naked eye finds it difficult to distinguish the individual hair roots. Fur is also usually finer in texture than hair.
Typically, fur has two or more layers: a short, dense, soft undercoat of barbed hairs and longer guard hairs. Fur’s function is to trap pockets of dead air, providing warm insulation for the wearer.