Game of Thrones author George R.R. Martin describes all the Targaryens as having silver hair and purple eyes and the show mimics his description as Emilia Clarke sports a white-blonde wig. But her eyes aren't purple. Daenerys is also younger in the books, like many others. She's only 13 at the start of the story. But the biggest difference may be her fire immunity on the show (and her hair's strange immunity). Martin has said plainly, "TARGARYENS ARE NOT IMMUNE TO FIRE!"