ColorSpace Transform OOTF

I need help with "ColorSpace Transform" OFX/Node
OOTF stands for Opto-Optical Transfert Function
What Opto and Optical refer to ? Wich one is "Scene" and Wich one is "Display"

I'll assume that gamma Rec709 is 1,96

ColorSpace Transform with those settings :
Input gamma : Rec709 & Output gamma : gamma 2,4 & Apply Forward OOTF Checked
does nothing ... why ?

ColorSpace Transform with those settings :
Input gamma : gamma 2,4 & Output gamma : Rec709 & Apply Forward OOTF Unchecked
does the same thing as this ColorSpace Transform with those settings :
Input gamma : Rec709 & Output gamma : Rec709 & Apply Forward OOTF Checked

Why "Apply Forward OOTF" is doing the same transform as Gamma 2,4 (Display) to from Rec709 (Scene).
It seems conter-intuitive ....

Then I understand the "Inverse OOTF" is the opposite of "Forward OOTF". So "Apply Inverse OOTF" seems also conter-intuitive ....

Please enlighten me
Thanks in advanced

I started writing an answer here but then deleted it because it didn't make much sense. I'll try to reformulate my 2 cents, but in the meantime, lets see what Resolve manual (omg, 4100+ pages!!!) has to say about OOTF:

SDR Rec.709: (default) Sets up a Rec. 709 SDR grading environment. Your work can be converted
to HDR on output, if specified, but is limited to a Rec. 709 gamut with out-of-bounds colors being
clipped. Gamma 2.4 is not mentioned in the name because scene versus display OOTF is managed
automatically. Suitable for conventional streaming and broadcast.
— SDR P3 Broadcast: Sets up a P3-D65 SDR grading environment. Your work can be mapped to
HDR for output, if specified, but it is limited to a P3-D65 gamut with out-of-bounds colors being
clipped. Gamma 2.4 is not mentioned in the name because scene versus display OOTF is managed
automatically. Suitable for wider gamut streaming and broadcast at SDR levels

Only mention about "opto" is in relation to opto-electrical transfer function. No mentions of opto-optical anywhere to be seen. Help section of Color Space Transform effect in manual omits the OOTF checkboxes mentions and descriptions entirely.

OOTF stands for Opto-Optical Transfert Function

Yes

What Opto and Optical refer to ? Wich one is "Scene" and Wich one is "Display"

Both refer to light, meaning physical scene (or virtual, makes no difference conceptually). On one end we have light hitting and captured by sensor, on other end light emit from the display. Sensor measures the light semi-accurately and OETF describes the relation between the light levels and stored values also semi-accurately, so we have an approximation for the mapping between the two described by OETF. EOTF describes the relation of signal values to emit light, but only in cases where this relation actually exists in some meaningful way. It only makes sense in the context of actual display, common example is gamma 2.4 calibrated screen where other quirks aside, EOTF tells that mapping from signal values displayed to emit physical light exhibits gamma 2.4 power law relation.

I'll assume that gamma Rec709 is 1,96

For clarification I'd always add that it is an approximation, because stating it as such is technically wrong, there is no gamma 1.96 in rec709 specs anywhere: "I'll assume that Rec709 is approximately 1,96 gamma corrected". Gamma vs gamma corrected means pow(input, gamma) vs pow(input, 1.0/gamma)

Thanks Hendrik
I agree with all what you wrote. I knew it and you confirm it

Again OP's questions remains. For me it's not logical. And I teach Resolve and this is the part when I say
"Learn it by heart"... because nobody (professionals include myself) can give a true logical answer.

It's not a big deal, I lived without any explanation and I can keep going
Thanks again