Arts in Ancient Greece

The conversation this week asked questions about why art from the continent of Africa can often be found in locations like natural history museums while works from the Greco-Roman tradition are kept and displayed in "fine arts" museums. Part of the discussion investigated distinctions between "art" and function. Another way to think about this is: What is the difference between "art" and "craft?"
As a musician, how do you feel about this division between art and craft? Does it make sense to you? Is this a real division? If so, how is it constituted? In order to answer any of these questions, it is necessary to give at least a short description or definition of what you see "art" and "craft" to be. This can be intuitively based, but provide a thoughtful start for your reader by determining this. Make an attempt to define each (but not using a dictionary). In music, is there a difference for you between art and craft? If so, what is it? Do some areas of music strike you as craft-based, while others are more about "art"?
When you conduct this discussion, take special care to treat each idea (art and craft) in a relatively straightforward way. (In other words, allow yourself not to choose sides in praising art over craft or craft over art, but attempt to understand each for what it is.) We are not asking for a ranking, but rather an assessment of the relationship between the two, in terms of how they play together, and if they can even be divided. Just look at each, and think about what makes one, and then the other, unique, or what it is; and appreciate each for what it is—just as we can look at two human beings who have different livelihoods, skin colors, and economic and social and religious backgrounds, but can still appreciate each for who they are. Provide examples to illustrate your ideas. Is there some aspect of music that seems more heavily rooted in craft? In art?
Your post should be two to three (well-developed) paragraphs long.