A painter is a businessman if he is intent upon making paintings which could be sold at the highest price. A painter who does not compromise with the taste of the buying public and, disdaining all unpleasant consequences, lets himself be guided solely by his own ideals is an artist, a creative genius. (Ludwig von Mises, Human Action, 240n5)
Though he is not a writer, Damien Hirst immediately comes to mind. He may at one time have been an artist -- but now he but a businessman. There is certainly nothing wrong with being a businessman (Shakespeare brilliantly pulled off being both), but if one is but a businessman, one's products will go the way of all other products in the past, and eventually disappear from the market. The work of the artist does not pass away this way (the ravages of history notwithstanding), but rather gains in value over time. Further, it remains a work of art, rather than being something of mere historical interest.