What is the difference between "brain" and "mind"?
Solution 1:
"Mind" refers to the part of you that is capable of thought. "Brain" can be a synonym for mind, and it can also refer to the physical organ within your skull. That is, the "brain" is a physical organ while "mind" is a more philosophical concept.
People sometimes make a careful distinction between the two words when discussing the philosophical concept. Like, when people are debating whether there is such a thing as an immortal soul, they will say things like, "Can the mind exist without the brain?"
In most day-to-day contexts, like your example above, the two words are pretty much synonymous.
Solution 2:
In many cases, there's no difference at all. Where there is one, it's generally that the term "brain" refers to the physical object inside your head while the term "mind" refers to the human capacity to think, sense, and process information.
So you wouldn't say, other than if you were joking or trying to make a philosophical point, "My mind weighs about 6 pounds." Similarly, you couldn't say, "I believe the human brain is actually a supernatural object where thought occurs and should not be considered part of one's physical body."
The substantial equivalence of these two terms flows from the well-known, biological fact that the human brain is the organ responsible for our ability to think, sense, and process information. For people who don't believe that, the terms become more different.