This is a very interesting arena of exploration! In actual experience there do seem to be different kinds of thoughts that we appear to have different levels of control over.
I'm guessing that at times you may have had the experience of a seemingly random thought popping into the mind and having quite a negative effect, resulting perhaps in some kind of aversion or anxiety or anger. In that case, you probably didn't choose to have that thought - "oh, let me think something that's going to make me miserable for the next couple of hours!"
But what we DO have some control over, is how we relate to the thought. So if we can see the initial unhelpful thought as just a thought and not buy into it (as in Session 7 of The Basics: “Keep it Going”), then we are learning how to use mental processes in a skillful way that simultaneously reduces unhappiness and increases happiness.