There are many philosophical problems that have moral implications, one of which is distinguishing between the brain and the mind. From a medical point of view the brain is just a bundle of nerves, another organ to be studied, diagnosed and dissected; the mind is of no real interest. A psychiatrist on the other hand might argue that the brain may be an organ, but the mind is not. Instead it is a barely detectable imprint within the brain, such that a man may be mentally ill without anything being physically wrong with the brain. The psychiatrist may also argue that a mind is something you develop, that we may be born with brains, but we are not born with a mind, that "a mind of your own" is something that comes later. Perhaps he may say your mind is a collective abstract containing your identity, personality, and experiences, the things that make you who you are. He may even cite a man in a coma and say - "See that man, he has a brain. It keeps him alive, but where is his mind? It is gone!". But the doctor (and the man's relatives) would pull him up on that point, suggesting that just because he is not moving, it does not mean that he is not thinking. Of course the opposite could be argued; just because someone moves, does not mean that they have a mind - maybe everyone except you is a robot! Which would bring up the question that if we could make them, would robots have minds, or even: do animals have minds? But I digress.
One illustration of the psychological difference between the mind and the brain is in the words we use in conjunction with them, for example, we could say that someone has "lost their mind" but to say that they have "lost their brain" would sound quite odd. Conversely one could say that someone is "brain dead" but not "mind dead", which brings me, in a round about way, to another interesting twist in the mind / brain debate. We could probably agree that a bee or an ant has a brain, but if I was to ask if it had a mind I don't think many people would say yes, but, it is not uncommon to suggest the concept of a "hive mind", and an acceptance of this really would indicate a distinct physical difference between the brain and the mind, for the hive does not have a brain.
In this argument viewpoint is very important, I know I have a mind, and I think that I have a brain, but do you have a mind? I don't know that - even though you would try to convince me you have, I can only guess that you have a brain. In fact, my own mind is the only thing I can be sure of!
To conclude, it seems to me that the brain is an immensely complicated, yet definitely physical object. But the mind, on the other hand, is not a physical thing at all, but in fact a vague concept, that will probably remain the subject of argument for many, many years.