So in psych 201, we have had two quizzes and we are allowed to use our notes in taking quizzes. I have to ask. What if my notes have the answers? Which they have actually had since I write down definitions and as much important stuff as possible. Is that not cheating? We can’t use notes for the unit tests though.
Sounds like good note taking and not cheating to me! 
Your notes sound like the ones I used to take. It’s not cheating if you write down the definitions of the terms during the class, those are your notes. If you make separate notes for use on the quizzes that are not what you did in class, then, to me, it’s cheating.
Well that’s the thing. We’re supposed to do our outlines at home. Outlines are chapters points, words with definitions, and whatever else is part of that. My note taking is done from the textbook. The notes being took from the textbook is what is being on a lecture.
If the prof wanted “notes” to mean anything other than “stuff you write yourself,” he or she would have said so. You take notes while you read, don’t you? (If you don’t, you should.) Those notes are notes.
The whole point of giving “open-note” tests is to get you to generate a good set of notes to study for the later exams from. At least, that was the point when I gave them.