Heart and mind are metaphors, but it isn’t clear exactly what for. @thorninmud says the mind is the prefrontal cortex. @marinelife calls it the head. Similarly, the heart is called by different names here, such as “emotions” or “fire.” @zenvelo throws in hormones and the body.
What we have are multiple decision-making and analytical methods built into us. Some we think of as being more cognitive—pure thought; and others we think of as being more automatic—chemistry.
I think it makes sense to think of having multiple “minds” that all discuss with each other (and sometimes argue), about what is the best action to take. Some of these decision-makers take very fast decisions and want to do things now. Others are more deliberative and careful and want to make sure everything is carefully thought through.
Sometimes we have time to think things through cognitively, and sometimes we will lose an opportunity if we don’t do it now! But if we take a fast decision, there’s a greater chance of getting it wrong. There’s also a greater chance of a big reward. If we make a carefully thought out decision, we may lose an opportunity, but we may also reduce the chance of making a mistake.
Our different minds see things from different perspectives and have different decision-making algorithms. They weight various considerations differently. That’s why they can seem to be telling us different things. In the end, though, we make a choice. Sometimes we change our minds—which almost literally means changing from one mind to another one that has a different decision.
It’s pretty complex, and I think we should value all of our minds, and not necessarily assume that the logical mind is any better than the intuitive mind or the hormonal mind. It would be a big mistake to assume that our emotions are stupid. All our minds are important, and by listening to them all, I think we make the best decisions.