> It's possible some students might call them professors, but it's not the proper term.
Some students? All students.
The usage of "professor" in the US is much like the usage of "lisp" in programming. There are many lisps (scheme, elisp,...), but there is only one Lisp (that is, Common Lisp).
Similarly, "professor" does indeed mean "Full professor". But students and staff in most universities call nearly all faculty "Professor X", whether they are assistant, associate, full, emeritus, adjunct, term, or whatnot. Indeed many US institutions have since invented official titles for, for example, instructors or adjunct faculty, which explicitly include the word "professor".
I became a professor a month after I got my PhD. Thus for my whole life I had been Sean, then for one month I was Dr. Luke, and then suddenly I was Prof. Luke. It has never been comfortable. I let the undergrads and some MS students call me Professor Luke -- I can't stop them -- but the PhDs, particularly those who are coauthors with me on papers, generally call me Sean.