IMO writing is the act of actually composing an essay/paper/composition. It's not the prep work, it's not the research, etc. If I saw you in the library reading primary sources, and I asked you what you were doing, would your answer ever be, "I'm writing a paper"? Surely not! Rather, I think you'd say, "I'm doing research for a paper." But, I don't keep track of our English-related subjects so minutely that I divide up these things. It's all English, IMO.