@MaddyDUMW this thread is from 2006.
I was a Math TA at IU in early 1980s. Back then, only courses in pre-calc classes (remedial Math courses) were taught by TA. Calculus and higher were taught by professors. In Calculus, 1 class were assigned 3 TAs who lead small group discussions. In the discussion class, I reviewed course material that I felt student would have a hard time to understand, answered student’s questions. Even though English is not my mother tongue, I have had repeating students in my calculus sequence classes. I believed I did a great job as a TA. TAs also had to hold office hours like professors.
Now I am working for a research University but not in a teaching position. I do see the changes in the area of teaching in Math where my spouse is a professor. I can’t speak for other subject. In Math, there are so-called instructors. They are given 5 years contract. These are individuals who hold PhD degree in Math. They only teach calculus or lower level courses. Even with these instructors, there are still some calculus classes taught by professors.
In Harvard, they are called junior faculty. No, I am not working for Harvard but I have a close friend who is a professor in Harvard.