I know exactly what you mean. To my, my form of internal visualization has always been more what some people consider to be their "mind's eye", but even that has a wide-ranging definition depending on who you ask. I like your explanation quite a bit more than just "mind's eye" though!

I can't "visualize" a full blown table, the example used in the article I linked, but I can imagine a very abstract form of a table. More like, if you were to take a modeling or 3D drawing program like Microsoft's Vizio and created a table in it, that's more what I can visualize. Or if someone asks me to imagine the sun, I can imagine a clip-art version of the sun, but I can't imagine vibrant brightness with it (another example used in the article).

Anything much more than that, and I'm no longer visually seeing it, but doing something more that you describe. As a random example, if you asked me to visualize a white neutron star, I can't literally see one in front of me - but it does make me recall memories of seeing one in the game "Elite: Dangerous".

I've heard theories (I don't know the accuracy of said theory) that when you're dreaming, your brain can't come up with something that's never existed - so when you see people, even random people, they're just random people you've encountered in your life but don't have any connection to. It's a sound theory for me, because that's how my form of mental imagery works, you could describe some totally fictional dragon as accurately and detailed as possible, but I won't be able to visualize it past a really abstract level. So if someone describes a purple dragon but gets really descriptive, I could visualize a generic animated dragon that is purple - probably would look more like Barney to me but... yeah.

Edit: Although that being said, I've noticed I'm a lot better at visualizing text. When I'm asked "How do you spell $some_word_here" I often find that I'm spelling it out-loud by reading out each individual letter. With programming, I find that when recalling something along the lines of "How do you make a function that does...", I'm using a combination of looking at a block of code I remember, and inferring the missing pieces.

I guess my brain is just weird...