This is a do-rag. Do-rags are usually made of synthetic, silk-like fabric. They have a form....they fit the top of your head, flow out in the back, and may be tied with two strings at either side. (The strings are just an extension of the fabric.)
Bandanas are squares of cotton fabric. A bandana COULD be called a do-rag if it indeed protects your (hair)do, BUT because true do-rags allow the hair to "breathe" while protecting it from the elements and being mussed, it is much better for your hair than a cotton square. They are different.
I am not sure what the difference is between those two and the biker headwrap is.