The main point of the brain dump is to write things down without thinking about them (too much). The next step is where you start thinking and organizing and categorizing and prioritizing. That's what gets you a good to-do list - and a good to-do list is invaluable for actually achieving your goals!
A "productivity system" is the name of the process and any tools you use to make sure you do the things you want and need to do. It might also be a name for something someone might sell you, all in the name of "doing more in less time". What's the simplest productivity system which will let you get a grip on your life?
According to Facebook and Pinterest, life is splendid, inspirational and good-looking. According to anyone you ask, yourself included, life is busy and overwhelming. But why are we constantly busy and tired?