There are a lot of discussions, especially among fellow designers over the difference between art and graphic design. The consensus is pretty much that they have different functions. Although they both deal with aesthetics, they serve different purposes. Graphic design is primarily about communicating visually. Art is concerned with the expression of the artist.
I agree, generally, but I think there's more to it. And I don't agree that art is simply an expression of the artist.
Art is universal, while graphic design is specific. What I mean is that art is producing something creative with great skill and ability. For instance, a programmer who does creative programming with great skill and attention is doing it as an art. On the other hand, graphic design is the art of producing commercial communication. That's why some illustrations are both graphic design and art. See the work of Howard Pyle or Norman Rockwell. Both have done commercial projects, but their work is also considered great museum-quality artwork.
Another difference is the intent of the work. Art is done for entertainment purposes (delight, repulse, enlighten, or thrill). Graphic design is done for commercial purposes (sell a product, idea, or brand). (Now, selling doesn't have to involve money, but it does involve active persuasion.)
Art's value is in the quality of the artwork itself. Graphic design's value is in the effectiveness it brings to what it's selling. If art fails to entertain, it doesn't achieve it's purpose. Following, graphic design must communicate a persuasive message to be considered effective.
Can art be used to sell an idea? I suppose so. But that doesn't change it's value as a work for entertainment. Art that sells ideas or concepts, but doesn't entertain, is usually called graphic design. But graphic design that sells ideas or concepts, and yet entertains can be called art (usually at some point in the future). See the work of Toulouse-Lautrec for instance.
Can graphic design be entertaining without being persuasive? Well, let me put it this way: If graphic design doesn't communicate what it's selling it may be nice artwork, but it certainly isn't effective design — which is the point of differentiating art from graphic design.