Shawarma comes from the Turkish term “çevirme”, which means ‘turning something.’ 

On the other hand, “döner” means ‘turning itself.’ 

In the past century, the rotisserie did not turn itself; someone was turning it, so Turks called it 'çevirme.’ But nowadays, it turns itself so Turks called it 'döner' whereas Arabs continued using the old Turkish term “shawarma.” 

Adding the word “kebab” (grilled meat in Turkish), means that “döner kebab” simply means “turning grilled meat.” 

This said, there are no differences between shawarma and döner kebab except those that individuals have created.  

At The Kebab Shop shawarma is a sandwich with soft fluffy bread. The döner kebab is wrapped in flat bread like a wrap. YUM.