Diffferent Types of Lucidity

I have a theory that lucidity does not lay along a one dimensional line, but it's more a place in a 2D or even 3D model.

Usually we think of it like this:

Non-lucid < semi-lucid (debatable) < fully lucid

But, not only do we have awareness of whether we are dreaming or not, there are different types of awareness: awareness of the physical plane's existence, and awareness of physical input (for example we have to pee in waking life, and we have to pee in the dream), and awareness of self.

Awareness of the physical plane's existence
We can forget about the existence of the physical plane in a dream, so that it feels like our whole life. (These can be lucid or non-lucid.)

Immersion
Let us call the inverse of awareness of physical input immersion, because if we are fully immersed we will have no awareness of physical input, or bleed over from the waking life.

Self-Awareness
By awareness of self, I mean having a state of sentience in the dream. In other words, you are making deliberate decisions, and not acting on autopilot (which is different from awareness of dreaming.)

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So, we can have different combinations of these states.

I am sure you have seen in your own dreams or by reading others' DJ's similar states. Are there other types of awareness that relates to dreaming?

What have you personally experienced?