Question: What exactly is the difference between the physical mind and the intellectual mind?

Sri Chinmoy: The physical mind is always limited to the boundaries of the physical body and its activities. It does not think of what is happening in far distant places or in some inner world or in the skies. This mind constantly thinks of what you are going to eat, what you are going to say, what clothes you are going to wear and so on. The most limited, gross daily activities are the realm of the physical mind.

The intellectual mind does not take care of anything in the physical world. It reads books and thinks of world politics and performs abstract mathematical calculations and that kind of thing. It is one step removed from the purely physical consciousness.