They simply aren’t the same.
The brain is the organ of intellect. Being an analytical, calculating organ, it naturally produces writing in an analytical, calculating manner with the aid of a critical, discerning eye. The brain knows when writing is technically good and flows in a logical manner. It produces literature according to rules and intertwined formulas, acting together to create a story with the necessary amounts of exposition, characterization, dialogue, literary techniques, etc., all with adequate clarity. For years the brain is drilled to learn how to write a particular literature for a particular audience, and with practice it can produce like a machine.
Heart is a word of many different definitions, whereas a brain is merely a thinking thing. The heart is a four-chambered pulsating muscular organ that circulates blood throughout the body. The heart is the center or core, and in Latin, it is appropriately termed cor. Some say it contains the soul, and many see it as a source of various passions and characteristics such as courage, affection, fear, and wrath. The heart writes for the sheer passion and joy of writing. The heart needs no monetary incentives, and it needs no audience. It cares naught for logical structure or pleasing aestheticism. One who writes from the heart just writes and writes and writes as faithfully as the organ beats.
The heart-writer does not require meticulous rewriting as a brain-writer would. Only “more-writing.” No obsessive editing and absolutely no perfectionism. The heart is honest and straightforward. The brain — paranoid and cautious in what it writes, and it must weigh all possible effects a written work might bring forth. It is arguable that the heart draws the body to write in the first place. It is the brain that determines to write better. One runs on pleasure, the other on labor, and the two work or fight together to form a very complicated relationship. Perhaps the heart will always dominate. Maybe the brain will rise in power. And there is the grim possibility that the two will always be at war with one another and one’s writing will therefore fluctuate immensely throughout life.