What is the difference between monopoly profit and monopoly rent? I understand that monopoly profit is the return on capital (=profit) of the monopolist, which is larger than the normal profit in a competitive market.
As monopoly rent I understand the income in excess of the factor cost (=rent) of the monopolist.
In this sense both would refer to the same thing.
Is this correct?
Economic (not just monopoly) rent is what is otherwise known as produces surplus. And producer surplus is related to profit via 

$$\text{Producer Surplus}=\text{Profit}+\text{Fixed Cost}$$

assuming that fixed cost is sunk.