Which style best describes your art? My definition of a "classical artist" is one who follows in the footsteps of the old masters. Someone who spends time studying and copying their work in order to create his or her own work along the same kind of lines. It usually involves painting timeless and traditional subjects such as: still life, portraiture, landscape, figure painting, religious, historical, and, mythological scenes.
On the other hand, a modern painter is one who isn't much interested in the art of the past, but instead seeks to learn modern methods and styles of painting that reflect modern life and appeal to modern sensibilities in subject, color, and design. Perhaps "commercial artist" might be a better term for this kind of painter.