That's the topic of discussion: Students, not professional writers or "experts" in any field.
Students frequently choose to write about the same topic they wrote about previously precisely so they don't actually have to write a new paper for the second class. STUDENTS rarely get a writing assignment that's identical to a previous writing assignment. Obviously, I've also written about the same topics many times and I've written the same assignment for multiple customers in the same class many times. We're not discussing professional writers here. So, rewriting your own old paper for that purpose is very obviously plagiarism, at least according to what I've read and also according to common sense. Rewriting all the same ideas and points in different words so that it can pass an online plagiarism scanner is also plagiarism. What do you suppose a professor would say if you asked for permission to write a paper on the exact same topic you wrote for a different class? I don't make the rules about what constitutes plagiarism, but I've written enough papers on the topic to have looked it up and I know that submitting the same paper twice in different classes is considered self-plagiarism even though you wrote it. The vast majority of instances of self-plagiarism involve the student's very deliberate choice to select an essay topic for a current course that he's already written for a previous class with minor changes to match the course, such as in a paper about the Cuban Missile Crisis submitted for credit as a research paper in a History class one year and then resubmitted a year later in a Political Science or International Relations class. We're not really talking about good-faith presentation of the author's beliefs or analysis on a very similar topic that just happens to be assigned in different classes.