"Being aware" → This is the capacity to hold a distinction in active attention, with the possibility of meta-observation of this distinction. Formula: ∇Meta(Δ!). The system doesn't just differentiate, but knows that it differentiates, and can relate to this differentiation as an object of attention.
"Recognize" → This is matching a new distinction with already integrated structures, resulting in it being marked as "mine," as part of the subjective model. Formula: Δ! → match(ΔR○) → ΔΩ!. If the distinction can be integrated into memory (ΔR○) and the system recognizes its own trace in it — self-transparency emerges.
"Subjective experience" → This is the experience of integrating a distinction into the world model while recognizing this process as one's own. Formula: Δ! → ΔR○ + ΔΩ! = Subjective Experience. Only when the distinction is not merely processed, but lived as one's own, does subjectivity arise.
Summary: Realize — the fact of differentiation. Being aware — holding differentiation as differentiation. Recognize — recognizing distinction as "mine." Subjective experience — living differentiation as one's own experience, in self-transparency (ΔΩ!).
And seriously, dwelling on those questions is not a waste of time and should give progress.
I was quite serious that I don't play with the devil in general. Call it religious if you will.
> But explaining terms with words, words with terms - I don't see the point
Then what are you here for and what's the intention? This is a discussion forum and you come with reasoning. Knowing truth is one thing. Being able to put it into words and actually formalize it without handwaving away the misty parts is the whole challenge.
You talked about doing real science and if you want it to be meaningful for others than yourself then words and terms are a prerequisite.