Estimates are statistical by nature; they are made of "educated guesses" and historical and empirical data available. Estimates must be unbiased. They are unnegotiatable and they are not commitments.
Plans are not statistical. They are oriented by estimates, but they must present concrete dates and, when they are not met, the plan must be revised and renegotiated. Plans are commitments.
I think this separation brings useful implications and tools to argue sensitively with stakeholders. I've always hated having to commit to hard dead lines based on estimates. While I was aware of the importance of providing concrete deadlines, it felt like I was taking the entire risk of the estimate for myself, which is unfair, to say the least.
By making the separation between estimates and plans, I'm more equipped to discuss the matter. I can show the estimate and, when pressed to commit with a tighter deadline, I have some leverage to trade the desired deadline for a decrease on the project requirements set, for instance.