Exploratory writing and thinking

Exploratory writing and thinking are obviously almost one in the same, but when you think about my teachers quote " Perhaps you think about things in this way without using writing as a tool through which to process your ideas." You are able to understand the literal diffrence of the two. IF one person starts to think about a subject and starts to brainstorm in their mind, what is there to keep them from forgetting their original thoughts. I have a short term memory and if I am constantly thinking about new ideas and thinking more in depth about a topic, I will forget something. This used to happen to me all the time. When a teacher would assign me a great topic to write a essay and I had so many ideas, I would just think about all the things there are to write about and by the time I got to my room, after all my other classes, I would forget half of the ideas. That being said, I soon learned that I can write these ideas down and save all of my thoughts.

But is that exploratory writing? Is that just brainstorming? What defines the difference, after all I was not writing to explore, I was writing to save my ideas. But my ideas could be thought of the same way, If I took the steps in exploratory writing, I could of found the same ideas and maybe they could of been in more depth. Maybe they would be just the same thing...