All fur is hair, but all hair isn't fur.
Hair may be related to reptile scales and bird feathers, which all represent different expressions of the same protein.
Hair takes even longer to decay than bones do.
Theories abound as to why people are hairless when our ape ancestors aren't. Temperature regulation? Pest control? Sexual selection? Or some combination: perhaps having less hair kept us cooler by day and kept the lice down, and we had clothing and shelter to keep us warm at night...thus allowing us to choose less hairy mates without our children freezing to death. Or something.
If you google "hair evolution", you get a lot of funky hairstyles, and a lot of beauty products with the word "evolution" in their names.