Brain is part of anatomy of a human being. Mind is the name given to functions of brain. So, though process and emotional reaction is called mind. This is like tongue and speech, eyes and sight, legs and walk.
Thus brain is part of our body. Mind is how the brain works. Brain is likened to hardware and mind to software although this comparison is not totally correct.
This is a good question. I read the above. Still I want to write in my own way.
Brain is an organ within which mind exists. Brain without mind is useless. Brain is made of cells. Mind gets developed and nourishment from the circulation of blood and pure oxygen. These helps in carrying out all activities of a brain. Mind is neither formed by cell nor it is an organ.