"Ο συγγραφέας γράφει ένα βιβλίο."
Μετάφραση:The writer writes a book.
It's subtle and hard to describe even in English. An author is perhaps more 'artistic', while a writer is more likely to be performing the mundane service of writing for a wage or fee. So you'd usually say "the author of the book" but "the writer of the press release", for example.