Yes, it's mainly the conceptual part that is problematic. Although when drawing Bézier curves, for example, I also have problems with the execution, but I think they are also due to lack of visual thinking (the relation between where I click/drag the mouse and the final curve is totally non-obvious to me).
Indeed, as you assume, "former" and "later" don't pose any problem for me because I don't imagine anything visual at all when I evoke those concepts, I just think about what they mean in a non-visual way. But I can see why you would struggle if you think visually.
I guess the analogous weakness in my case is the one that manifests when I have hung my coat and forgot to take out e.g. the keys. I know what pocket my keys are in (e.g. suppose they are in the left inner pocket) but I totally struggle to find it when I'm not wearing the coat. Visual thinking seems to really outperform symbolic thinking in that problem, and sometimes memorization of the solution provides a shortcut in similar issues, but there it doesn't work because the coat can be hung in two orientations! So it's usually faster for me to take the coat, put it on, take the keys, and then hang the coat again, and in fact that's exactly what I do, at least if no one outside of friends and family is looking... :)
I'm not sure about learning styles (if a teacher provided a visual schema of a lesson I just translated it to words, or focused more on the oral explanation and ignored the diagram, and still learned it fine, it wasn't such a big deal as some people make it look like), but thinking styles are definitely a thing. I'm not sure if the difference is learned or innate either. In my case, I have always loved reading and read a lot since infancy, so it might be learned.