No, they are not.

The brain is a physical organ of the body, whereas the mind is an intangible concept that obviously bears some relationship to the brain.

(Note that someone can "lose his mind" without losing his brain.)

To repeat, we are not ruling out particular theories of neuroscience that claim that certain mental states are caused by particular brain states.

We are making the very modest point that mental states or operations (such as anxiety, happiness, long-range planning, multiplication, etc.) are different from brain states (such as firing neurons and blood flow to the left hemisphere).