We don't often see this word standing by itself, but it can cause confusion. A wright is one who makes or creates something, such as a millwright or a playwright. A person who is a play writer is not a playwrite, but a playwright -- one who creates plays. And although the legal protection is for what the playwright writes, it is not called a copywrite but a copyright.
Which leaves one wondering why if there is a playwright there isn't a wordwright instead of a wordsmith.