I think that it is a mistake to assume too close identity between brain and mind. My brain is a limited physical structure confined in a skull. But what is mind?
There is a one to one relationship between a brain and the mind that is associated with it. The term 'mind', when used in the context of 'a brain', generally is a reference to the behaviors, activities and abilities that make up a human's mental world, as in 'a mind'.
However, to ask "What is mind?" usually is seen as evidence that the questioner has, or wants to have, (or wants to debunk) a concept that 'mind' is a separate universal substance, process or entity that needs to be combined with a brain or produced by a brain in order to form a human mind. Imagining that a human mind can work without a human brain is a common response to fears about the perceived limited time span of a brain.
As a panpsychist, I see the universe as the process of being, which is a process with primary mental properties, that chooses and intends every form into existence. A human mind is this process expressing itself through a surrounding human form. The part of the human mind associated with activities of awareness, thinking, cognition, memory, etc., which is typically described as our conscious state, are a result of the process of being living through the human brain.
Before you express that reaction to my way of seeing reality, remember that we are both looking at the same reality. It is probably just my words that you don't agree with exactly. Some see the process of being but call it 'mind'. Some call it consciousness. Some identify it as 'life'. But if you try looking at what we are seeing and try to see how my words might fit what you are seeing, perhaps you can see some truth and we can both move forward.
Svetlana
I hope this helps. I am not really sure what level of answer you needed. Some of this might be a bit too deep.
I would generally agree with Frank (above). It is, based on the working definition of mind, to some degree, a philosophical discussion, and to some degree an empirical discussion.
When many people distinguish between mind and brain, they are using it in a dualistic sense where the mind is the modern version of a soul. In this case, I'm rather firm as an empiricist that there is no meaningful distinction as it invokes a "supernatural" thing which, by definition, has no grounding in a natural, observable, world, or in the work of scientific researchers.
There is another camp who use mind versus brain to describe the cohesive experience of reality, self-direction, and ultimately that of consciousness. In that use of the word mind, it is dependent on the brain and a direct product of its functions, but is considered distinct from biological sense of the term. There is some meaning for this term as a cell is distinct from the proteins that compose it, but all functions are utterly dependent on and can be described by those protein interactions. So in building the construct of mind, it is useful only to an extent that its composition allows. And, in that, no reason, other than personal belief system, to think there is more to a mind than what is contained within your skull and composed of your neural processes.
There is a whole body of evidence discussing this topic particularly among neuroscientists and those who discuss consciousness (Search: the hard/easy problems of consciousness). Wikipedia has a pretty good introduction to the topic which was proposed by David Chalmers, they discuss both the philosophical and the biological perspectives of the argument.
The argument usually evolves into a question of the existence of free-will. I have attached a link to an article looking at this from a neuroscientific perspective.
To boil down your question any further, you are going to have to provide some definitions and descriptions of what makes the mind and brain distinct.
The so-called 'identity theory' that the mind is the brain was developed in the 1950's. It is in principle sufficient to explain all experimental data thus far obtained from measuring brain activity.
That, however, doesn't mean that identity theory is acceptable. Two main arguments against it are these:
it discards free will as an illusion;
the brain is viewed as a classical system of particles - although this is enough for explaining the data, we know that classical mechanics is false.
Currently there is no consensus whatsoever on the mind-body problem, that is, on solutions to the questions "what is the mind?" and "how does it cause bodily motion?".