Brain is the hardware and the mind is the software with the totality in action, so the brain with mind is the hardware plus software.
MIND is a coherent (internally self-consistent) abstract system which converts signals from some sort of sensors into meaningful symbols or concepts (implicitly quantizing them), reorganizes them in light of known historical symbol patterns from its own unique symbol field, and converts them back again into signals for some sort of actuators. “Thought” is the name commonly given to the symbol processing operations of such a mind, when it is believed to be “conscious,” but perhaps a more liberal view is justified. A conscious mind is precisely the ability to use its free will to develop and assign symbols to inputs and outputs so as to create a meaningful symbol system with which to interact with the rest of reality. (The glossary in Mind Made Real). The way we describe things like "thought," "mind," "brain," and relate them with each other can cause confusion or ambiguity. We could make things clearer if we say that brains perform a variety of actions, and one of those actions we call "thinking."
Minds are learning systems. A mind is the subjective and qualitative aspects of a self-organizing system of energy in which the system builds models of itself and its environment in order to predict future patterns of experience. The keys to the success of model-building are memory, abstraction and categorization, so a mind is an embodied system that uses memory and abstraction to categorize experience. This capacity for mind evolved because there is a distinct advantage to continuous (minute-to-minute) behavioral adaptability. In other words, an organism with a "mind" is able to "evolve" from moment to moment, rather than relying just on the slow multi-generational evolution. The mind is being the subjective and qualitative aspect of brain. Maybe part of the confusion here is that equating brain and mind, forgets that mental events are conscious processes. It might be more accurate to say that brain processes are identical to mind processes. A brain that does not process, is not functional or alive, cannot necessarily allow for mental events to occur.
"Brain" and "mind" are labels for things distinct, but interconnected. Each brain projects something similar, but perspective, experience, sensitivity vary from individual to individual. The brain is an apparatus, a tool is wired for collective sensation and awareness. The mind is something more personal. It is a label that individuals create for that collective sensation or awareness that is on their own. The collective sensation is one's perspective, experience, memory, imagination, the world is projected by the brain through the collection of sensations and ideas that we are sensitive to and intrigued by. One’s collective sensation (mind) is not metaphysical, it is complex and not accessible by other one’s mind, so one can understand how others may deny the distinction between mind and brain. Although the mind is inseparable from the brain (inseparable, but not identical). When the apparatus (brain) ceases to work, so too does the collective sensation, much like what happens when you turn off an electronic device.
The "mind" is traditionally referring to consciousness or awareness. That consciousness is a feature of brain processes, the conscious processes are identical to brain processes, and perhaps that non-conscious processes are identical to brain processes as well. So both conscious and non-conscious processes are identical to brain processes. Consciousness emerges / transforms. Brain states transform. There are particular kinds of brain states and processes: non-conscious brain states, possibly sub-conscious brain states and conscious brain states. There could be more if there is a continuum between non-conscious to conscious brain state activity, which would mean that we have simply, in an arbitrary fashion, punctuated points in this continuum to select and name different brain states as modes of conscious processes; and emergence is simply the transformation of non-conscious/sub-conscious brain states into conscious brain states; and dissipation of consciousness relies upon the reversal of this process. So, the transformations of conscious states are identical to the transformation of particular brain states.
Brain is the hardware and the mind is the software with the totality in action, so the brain with mind is the hardware plus software. Mind is probably not brain in action alone. It may also be a whole-body phenomenon, with inputs from environment as well. So mind is much more than an active brain.