They're pretty clear that their thoughts are in language, and mine are not. I'm not sure how those can be the same thing. I can stop thinking thoughts, yes.
I agree with wilg. For example, what you are describing seems similar to my own subjective experience and yet, I've always thought of myself as having an inner monologue. To me, an inner monologue is just about reasoning in my head with the help of language. You are capable of formulating sentences in your head? Solving riddles? You can articulate how you reached a certain conclusion? etc. Surely not every word that comes out of your mouth comes as a surprise? I don't think having an internal monologue necessarily means having a constant conversation with yourself.
As I originally mentioned, I understand what you are talking about, but I just don't agree it's a real distinction. I believe people who claim to have an inner monologue and people who claim not to are having more or less the same types of internal experiences, they just describe them differently. As the Wikipedia article you linked to discusses, this sort of thing is difficult or impossible to study because it is a subjective experience within your mind. Since most of the research angles involve self-reported studies, it's highly likely that these differences are illusions created by trying to explain mental experiences with language that cannot capture it.
From the tweet I linked earlier:
> This is just an issue of these things being extremely hard to explain using language, and people using words in subtly different ways.