Do Exposure and Zone system use the same algorithm?

Hi folks,
Do Exposure and Zone system use the same value manipulation algorithm? I was convinced they are, but…
I’m observing different results applying them to the same region.

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Exposure works by multiplying RGB input by a constant equal to 2^{EV}, so for example, adding 2 EV results in a multiplication by 4, subtracting 2 EV results in a multiplication by 0.25.

Zone system works in Lab, scales the L channel logarithmically then split it in zones, which really does not make sense at all (EV readings from Lab are not EV). The next drawback of this module is you can’t push a zone without pulling another. The last but not least is, as usual, doing magic on the L channel messes up colors in a strange way.

I’m working on a tone equalizer that uses the same algorithm as the exposure but allows to define a different exposure compensation for each zone, then blends them using a gaussian series. It’s WIP, see there :

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Thank you @aurelienpierre I was hoping someone would answer my doubts. There is definitely a difference between those two.
Sadly there is no blend mode that can run Zone System in RGB scale. Do you happen to know is Zone System using gaussian algorithm to break down an image?

No, it looks like a sort of sigmoid function:

Thank you @aurelienpierre for your contribution. Your inventions keep pushing DT forward. I wish I was programmer and could help you with creation of Tone Eq, but I’m not. I need tone EQ very much. Let me know if any help is needed in non-programming tasks.