The split in one line
The creative director owns the why. The creative producer owns the whether — whether the idea can be paid for, staffed, scheduled and legally shipped.
When a project drifts, it is almost never because those two people disagree. It is because nobody said out loud which of them owns the decision on the table.
What each one is actually protecting
A director protects the argument of the film: the message, the pacing, the emotional beat that has to land in the first three seconds. Everything else is negotiable to them, which is exactly why producers get nervous.
A producer protects the conditions that let the argument survive contact with reality. Crew availability, location permissions, talent rates, render time, the contingency that covers a rained-out shoot day.
There is a third role people confuse with the first: the design director. A design director owns systems and execution quality. Merging that job into creative direction is how directors end up policing logo margins instead of writing.
How to write the split into the project
Name one approver per decision type before kickoff: concept, look, budget, schedule, legal. One name each, in writing, in the same document as the deliverables list.
Give the producer veto power over feasibility and the director veto power over intent. Neither gets a vote in the other's column.
Run one shared change log. Every scope change gets a line, a cost and an initial. This single habit removes most of the end-of-project arguments I have seen.