This topic poses no clear philosophical question(s), it’s just me examining something that intrigues me. Axiomatic (i.e. assumptions; (hopefully-educated) guesses):
Mind exists. Mind entertains thoughts and thinking.
As a retired software designer, with my speciality being firmware, I find it natural to begin with the hardware and work upward in abstract levels. In this case, my use of “hardware” is thoroughly figurative, as mind has no physical (the “hard” in hardware) existence that I know of.
The first level we encounter is the most basic. Almost everyone thinks in words, pictures, or some combination of the two. I think in patterns, which is unusual, but not unheard-of. Perhaps there are other variants of which I am unaware? It would be interesting to find out…
Does our internal ‘thought language’ (words, pictures, etc) influence the way we do philosophy? I think it must, mustn’t it? 
At the next level, we find one of the most basic thinking styles: binary thinking. Fight-or-flight thinking. In our earlier history, this was what we needed. Without it, the survival of the fittest probably wouldn’t’ve included most of us. 
Binary thinking seeks to simplify everything to a simple two-way decision. TRUE or FALSE; black or white, fight or flight, and so forth. When you’re not sure what that noise was, you don’t have time for philosophical deliberation, so this style of thinking is thoroughly appropriate to our needs at that time.
But there are other styles of thinking too, the most obvious complement to binary thinking is multivalued thinking; flexible thinking; systems thinking; network thinking; gestalt thinking. Such styles can be more powerful than binary thinking, in some circumstances. In some cases, there are issues that binary thinking simply can’t deal with. In other cases, not so much. It’s always about selecting the most appropriate tool from your toolbox: horses for courses, as they say.
Up another level, we might discover seeming ‘types’ of thinking: logical/rational, emotional, team/faith doctrine, sociocultural or personal, the list probably goes on… Not all of these are useful to philosophers, but they are styles for which we find uses, in various aspects of our lives.
As we rise in (abstract) levels, the term “thinking style” gradually seems to become less useful and relevant, but I think we have at least one more useful level. The contrast between certain and ‘objective’ thinking, such as a scientist might do, and flexible and uncertain consideration. Again, these tools are appropriate for some tasks, but not so much for others.
As a final offering, we might consider a focus on ‘law’ or on ‘chaos’. Or a more inclusive view that tries to consider both, perhaps as some sort of spectrum.
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So, is there anything here that you find interesting, and would like to discuss? I hope so. I await your judgement.