These are the main differences that I simplified. Hopefully everyone can understand this now.
Designer = Mockups - using something like Sketch to make it look beautiful. Conceptual. Kinda like a painter or architect.
Backend Developer = Does all the server side and database stuff (python, php, ruby, NodeJS, MySQL, Mongodb, Postgresql etc).
Full Stack Developer = Does both frontend and backend development.
Unicorn = Full Stack Developer + Designer. Good luck finding one.