A. C. Grayling tries to make a distinction:
Minds are not brains. Please note that I do not intend anything non-materialistic by this remark; minds are not some ethereal spiritual stuff a la Descartes. What I mean is that while each of us has his own brain, the mind that each of us has is the product of more than that brain; it is in important part the result of the social interaction with other brains. As essentially social animals, humans are nodes in complex networks from which their mental lives derive most of their content. A single mind is, accordingly, the result of interaction between many brains, and this is not something that shows up on a fMRI scan. The historical, social, educational, and philosophical dimensions of the constitution of individual character and sensibility are vastly more than the electrochemistry of brain matter by itself. Neuroscience is an exciting and fascinating endeavour which is teaching us a great deal about brains and the way some aspects of mind are instantiated in them, but by definition it cannot (and I don't for a moment suppose that it claims to) teach us even most of what we would like to know about minds and mental life.