I concur with your point about the programming model and style, but I do also maintain that "cooperative" vs. "preemptive" is not about that difference. It is a technical difference on how the system interleaves threads and whether it needs cooperation from the code running on them, and not on the programming model and critical sections.

For the distinction you have in mind, I see the terms "colored" vs. "non-colored functions" to be used the most, and they are both within the "cooperative multithreading" space.