There are similarities between fine art and graphic design but for the general public there are more differences.
Most often, fine art is thought of as exclusive. To view fine art one would expect to go to a museum, gallery, or exhibit. Fine art is studied in depth and is very emotional. Many artists put their heart and soul into whatever medium they work with and when others observe the final product they can feel the emotion and it moves them. I think many people view artists as highly skilled, and creative. The mass public does not own clay to sculpt or paint to create a painting. One thing the mass public does have however, is a computer. Fine artists work in mediums that are not household items. On the other side you have a graphic artist that uses design software on the computer. I think the reason graphic artists seem less artistic is because of the medium used. People think if they can do it, I can do it.. after all, it's just a computer!
Another difference in fine art and graphic design is for the public to see graphic design they don't have to leave their home. Graphic design is on junk mail, magazines, tv commercials, and products in their home. They might think a design looks cool but I doubt they stand around pondering on the design as they would a painting. One reason for this is because they don't have to ponder what the design means. Graphic design is very straight forward and intentional. Most designs are created to convey a certain idea very quickly.I think it all comes down to information vs. appreciation.
I think graphic design is an art form but there are many things that separate it from the fine art world. Graphic design became more of an art form in my eyes when I learned the principles behind design. I enjoy looking at graphic design as much as fine art now.