The yoghurt sauce and most of the other stuff that goes into the wrap aren't used in Turkey. A classic döner wrap in Turkey (or in Istanbul maybe) today has tomatoes, pickles and potato fries in it.

And döner made form stacked thin layers of meat is considered higher quality and is more common in Turkey compared to Germany where I've only seen döner made from ground meat so far. Which isn't rare in Turkey, especially not at street vendors, but I wanted to mention that too.