I normally find that Jennifer Borenstein offers excellent college advice in her “College Corner” column in the Davis Enterprise. Unfortunately, however, her most recent column is misleading, both in its use of terms and in the elephant in the room that it leaves out.
First, do TAs teach college classes? Occasionally, but not in the way that Borenstein means.
To be (perhaps excessively) clear, a graduate student is a person who is pursuing a degree beyond the undergraduate (BA, BS) level. Once someone is a graduate student, they might be a teaching assistant, or TA. Or, they might be assigned to be a primary instructor for a class (sometimes with graduate student TAs!). Or, they might not teach at all. Thus, in the usual case, it doesn’t make sense to say that a TA is teaching a class. If a graduate student is hired as a primary instructor for a class, they are not a TA. They are the primary instructor.