Perhaps I should be thinking of it like painting; You can say "I am creating a painting" or you can say "I am creating an abstract painting". In then same way then, you should be able to say "I know a martial art" or "I know the martial art of Taekwondo". The more deeply you go into naming it, the better an idea the person you are talking to will have of what you do. Taekwondo is a martial art, Chung Do Kwan is a style of Taekwondo, and the school I go to has a particular look upon the style that is unique to any other school. As far as Karate goes, are the different styles similar enough to be considered the same form of art?