Diaper was originally the term used for an overall pattern of small repeated geometric shapes, and then a white cotton or linen fabric with such a pattern. So the first babies' diapers were made from diaper fabric, meaning fabric with a repetitive pattern.  A "nap" is a hairy surface of cloth formed by short fibers; it was the preferred material to make "nappies".  The word "diaper" is used in America and most other countries that speak English, while a "nappy" is used in England, New Zealand and Australia.