Brain - noun: an organ of soft nervous tissue contained in the skull of vertebrates, functioning as the co-ordinating centre of sensation and intellectual and nervous activity.
Self - noun (pl. selves): a person's essential being that distinguishes them from others, especially considered as the object of introspection.
The New Oxford Dictionary of English
The mind is a product of the brain, and the self depends on the mind, but understanding them requires different approaches. The following analogy may help to draw out the distinctions. I am using a PC to type these words and they appear on the screen by virtue of the wordprocessing software and the computer's electronic microcircuitry. Detailed knowledge of the hardware is of little help in understanding the software, and vice versa. Hardware and software are both irrelevant to the content of the text. Think of the brain as the hardware, the mind as the software and the self as the text on the screen. The text could be anything - a guide to sea fishing, a suicide note, or a Japanese haiku poem. In fact, why not a haiku?