To me, thoughts appear as relationships or associations. When I think of something, I remember something else related to that, and then the next thing, or several next things. All these memories are at first very vague - more like feelings - and then if I give one of them attention, it becomes more specific. Now, if I look more carefully at a single thought - it is not a solid thing, it is just a pointer to more memories related to it. So to me all thoughts are empty connections with one another.
I can also visualize objects as images, and sometimes these visual images float from memory all by themselves - so some of my thinking is visual. Or sometimes I remember sounds or tactile sensations. But those are more like "memories" than "thoughts".
I also have inner dialog at times, but by now I have mostly learned to stop it when needed. So when I think I mostly don't think in words, but in those connections I described above. When I do have an inner dialog it sounds like memory of my own voice, i.e. like I'm talking very quietly to myself, or rather remembering how my voice would sound if I said those words.
When I think about something complex, organically (i.e. not reasoning step by step), I may have some kind of complex interconnected structure appear in my head. It's like a mesh of interconnected wires, each wire being a thought connected with other thoughts. Sometimes I look at the entire mesh from afar and try to see high-level patterns, or a particular way seemingly unrelated things are connected. This entire structure is multidimensional, not 3D. Sometimes two thoughts may appear as two separate thoughts, but if you trace them into another dimension you will see that they are in fact two projections of the same one thought and that's how you see they are connected.
Working with these thoughts-as-connections requires using feelings. Feelings are like queries you can send to the mesh, to find relationships, or to find a particular thought.