Crafting and DIY have a lot in common, but they can be distinguished in one basic way: Do-it-yourselfers typically create, first and foremost, for a tangible purpose, while crafters typically create, first and foremost, for the sake of creating.
The character of crafting became what it is today in the wake of the Industrial Revolution, when suddenly everything was mass produced and the necessity for individuals to build, sew and create their own décor, clothing and furniture fell away. Many of those who missed the act of personal creation turned to crafting.
In this way, crafters are artists: Creativity is the driving factor. Family chronicles or warm legs or a dresser that finally matches a home's look are happy outcomes -- if they come out at all. A "failed" project, in crafting, is viewed by most people as no failure at all if it facilitates self-expression or experimentation or simply satisfies the human urge to makesomething.
This, then, is the common thread between crafters of yesterday, today and around the world. Other traits, though, are less universal. And considerably more practical.