difference between the Exposure, Black Level, and Brightness controls

Hello Glenn Butcher,
thank you for your mathematical formula, but unfortunately it overwhelms my understanding.
May I ask again, what exactly does the slider “Black” do? I have seen that it is excellent for making a photo that is too dark lighter and friendlier if you move “Black” to minus. All tonal values remain (for a long time), very similar to the “Brightness” slider. Only if you move “Black” to the positive range, the dark grey areas will quickly turn black, which sometimes looks good.

So my question: Is the function of the “Black” slider in the minus range about the same as the “Lightness”? Or is “Black” just meant to make darker areas even darker, to summarize them as black?

kind regards
micha