To avoid constantly generalizing from one example when it comes to human thought, I think we need a survey of the ways people can reflect on their thought process, as subset of the ways people can think.
Before having heard of the Francis Galton's study on the imagination I assumed that everyone thought in the similar way to me (except be better or worse at it), and would be puzzled why some people would believe in e.g. strong version of Sapir-Whorf hypothesis. (I couldn't even understand how they can not realize that to make even remotely coherent argument in support of this hypothesis they would have to be thinking outside the language - or so I thought)
There may be a very significant variation in how human thought process works, and how much of the process is accessible to reflection. In Richard Feynman's What Do You Care what Other People Think? he explores a technique for tying up part of the thought process by mentally counting, and exploring what sorts of thinking interfere with the counting. (I can't right now find a good online quote from those chapters and I do not have the book at hand to directly search; perhaps someone can help?)
I propose we describe the ways we believe we think, along with relevant self-observations supporting those beliefs. Just as a first step though - to get very rough idea. Note: lack of ability to reflect on something does not imply lack of function.
Then based on the responses we can form some hypotheses and make a proper survey perhaps to be combined with some set of cognitive tests. You perhaps should stop reading right now if you don't want to be primed with my own self description, but given that we all probably have been exposed to great deal of descriptions of thoughts the priming perhaps is not a big problem here.
So, for me, the distinct modes of thought (ALL coexisting in parallel at any time, except for the mental visualization which I am not using when I am busy using my eyes). The order is not related to importance:
1: Auditory based 'internal monologue'. This is like talking to oneself - e.g. i use it for counting. Observations: I can have internal monologue counting the seconds (as described by Feynman), and while i'm doing the counting i can't put thoughts in words or talk. That's the same for either English or Russian. Observation: right now i am internally 'hearing' the letters I am typing. When I stop typing I can imagine hearing "the ride of the valkyries", but I have difficulty doing that when I am typing. I can play back music when I am reading though. For some time shortly before falling asleep I can sometimes play orchestral music in my head or make myself 'hear' a song with utter unreal clarity, but not normally.
I can also use 1 to serially check something for validity.
2: Mental visualization. I use it a great deal for engineering related tasks and to big extent for math (e.g. if i need a function that does something i'll be thinking in terms of images, if I am thinking of an algorithm i usually employ imagery, etc). Observation: I am right now imagining a beach with waves crashing onto sandy shore. As I stopped typing I could imagine the sounds of the scene. This mode of thought is somewhat less subservient; i may be unable to get some images out of my mind at times. For me mental imagery interferes to some extent with visual processing of real world stimuli. I pretty much always have mental imagery when I am reading books (the ones evoking any imagery, at least). The mental imagery is not very stable. I can't visualize full rubik's cube in arbitrary position well enough to solve it in my head. I can visualize chessboard, but I never tried actually playing chess blindfolded and I don't think i'd do well at it.
3: Some weird logical inference type thought that is neither in a language nor visual, works by referencing what things are rather than word labels; it has no problem attaching what ever properties (like list of logical dependencies or feel of 'likehood') to statements. That's what I try to think rationally with.
Observations: As I am composing this message my verbal thought is tied up, and I can easily tie up visualization by visualizing the beach scene right now; at the same time I am thinking freely as of what points I want to discuss, and this seem not to be done in any particular language or conform to structure of language. I regard it as 'what I am really thinking' and I can only reflect on it with 1 second delay or so. Literally. I don't know what I am really thinking right now - I know what I was really thinking 1 second ago. I don't normally even reflect on 3. The 3 really easily gets distracted to thinking about unrelated things when I try to do some work.
3 seem to work at high speed. That's the kind of thoughts that I recall running through my head as I stumble or accidentally toss a cup off table and catch it (or not catch it).
If I invent or reinvent something, I think of it without having a word for it, and its a chore to choose good descriptions (such as name the variables and functions when I am working as programmer). Sometimes I am stuck being unable to recall a word; the reference to what the word means is in my head but either the word does not pop up, or the word that pops up is in the wrong language, or is not good enough fit and I feel a better fitting word is available. When programming I tend to think in terms of reference to what a function does, but often have trouble recalling how I named that function (I guess what I could've named it).
4: Insights, when solution to a problem just pops into my head with zero data about the process that arrived at this solution (even though the solution would come complete with the data to tell that its a good solution, I can't see what alternatives were considered and rejected). This seem however not substantially different from how the thought gets from one step to the next step; just takes longer time. Memories can pop up in similar fashion.
5: Well trained kinetic stuff. Observation: I can juggle while reading text off a page.
For me the 3 seem to be the weird one. 1,2,4 are often described in literature, 5 got to be quite universal. I can barely reflect on the 3 at all, and only with 1 second delay.