If a Copywriter is words, then an Art Director is pictures. As an Art Director, you don't have to be a fine artist yourself. But you have to be knowledgeable, have design and taste so that you can live up to your title. The Copywriter There is not much specialized training for a Copywriter. Outside of perhaps a B.A. in General Arts or Journalism, there are few courses to take.
Copywriters master the English language.
A Copywriter needs overall life and people skill experience. A general knowledge of many things. Experience in newspaper, magazine or broadcast writing is helpful. Even working in a retail store or as a taxi driver. You need experience that will help you write convincing copy.