Both Graphic Design and Fine Art are both art related, but there very different meanings. Fine Art can be categories in many different art forms. For example, like painting, sculpting, dance and so on. Graphic Design is mainly images and typography as one that give the viewer visual communication. So there is a difference.
Graphic Design goes way back in human history. One of the earliest forms of Graphic Design is pretty much the time of the cave men with their cave pictures. With the invention of the paper visual communication became big. And by 20th and 21th century graphic Design had began bumming. Today Graphic Design is practically everywhere. In magazines, television, logos, posters, streets and pretty much in the web. You can go anywhere without see an ad that will smack you on the face the moment you see one. In History the tool that use for designing had change in time. It started with Chisels, then brushes, then pencil, and finally a mouse.
What I explain previously Fine Art has different views in art. Visual Art is primarily for aesthetic purposes and judged for its beauty and meaningfulness, specifically, painting, sculpture, drawing, watercolor, graphics, and architecture.