The way you’ve described the difference here makes perfect sense to me. I didn’t quite get that same message from your story. You described the differences as:
1. Method of acquisition
2. Who dictates the terms
Yet none of those things are unique to customers over clients.
I agree with the point about the difference in creative freedom. Although I don’t consider my clients “bosses” because it’s a partnership, there are certainly more constraints in client work. I find those constraints breed creativity and the challenge of working within new constraints on each project is what makes client work interesting.