As Johansen mentioned. Description can be found in the manual.
Tone Mapping Method lets you enable tone mapping to accommodate workflows where you need
to transform one color space into another with a dramatically larger or smaller dynamic range by automating an expansion or contraction of image contrast in such a way as to give a pleasing result with no clipping.
— None: This setting disables Input DRT Tone Mapping. No tone mapping is applied to the Input
to Timeline Color Space conversion at all, resulting in a simple 1:1 mapping to the Timeline
Color Space.
— Clip: Hard clips all out-of-bounds values.
— Simple: Uses a simple curve to perform this transformation, compressing or expanding the highlights and/or shadows of the timeline dynamic range to better fit the output dynamic range. Note that the “Simple” option maps between approximately 5500 nits and 100 nits, so if you’re mapping from an HDR source with more than 5500 nits to an SDR destination there may still be some clipping of the highlights above 5500 nits.
— Luminance Mapping: Same as DaVinci, but more accurate when the Input Color Space of all your media is in a single standards-based color space, such as Rec. 709 or Rec. 2020.
— DaVinci: This option tone maps the transform with a smooth luminance roll-off in the shadows and highlights, and controlled desaturation of image values in the very brightest and darkest parts of the image. This setting is particularly useful for wide-gamut camera media and is a good setting to use when mixing media from different cameras.
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These options are really just a matter of relativity and convenience. They are not color grading tools per se, just few convenient sliders in the same node. They are not meant to replace a set of other grading tools or decisions made by colorist. In that sense they are both relative to the context of what you are doing and optional since there are other tools that can do the job. And there is a matter of where in the pipeline the tool is used or where in the node tree it is used. You could have CST applied in edit page, fusion page, color page, multiple times, plus all the other tools, and for different assets on the timeline and or fusion. Sometimes you want and sometimes you don't want tone mapping. Only in the most simplistic cases would you use CST once with those options and never look back. That is not always the case, so we are given lot of flexibility. The examples you posted should't be used to asses tone making options of CST tool, because of those reasons.
I've given a link in another thread where you asked a question about out of gamut colors.
viewtopic.php?f=21&t=212651https://juanmelara.com.au/blog/fixing-o ... in-resolveAs you can see from these two example bellow: CST node or nodes and tone mapping is just one small part of a much larger process of grading, so what they do is useful to know, but its not set it and forget it tool for finish grade. Depending on your source and output, and personal workflow, CST is just one tool in the toolbox. Here are ways how it might be incorporated into more complex workflows as demonstrated by colorists Juan Melara in these videos.
Insider Knowledge - An easier way to grade log footage
The Kodak 2383 LUT rebuilt as a Resolve PowerGrade