Usually a game designer writes out the GDD, does the planning and scheduling as well as translate from programmer to artist
The designer is the top guy on the project with exception to the people supplying the money. on a project to project basis they are sometimes known as a project lead but on a career basis they are game designers.
It becomes a lot easier to remember if you look at it as software rather then games. then you have :
Software Design - Think of a application
Software Development - create the application