Your dual ISO diagram is wrong. At least in terms of the technology used by most photography cameras and invented by Aptina. During exposure the photodiode is acting as a capacitor and building up an electrical charge. A dual gain sensor has a second capacitor in parallel with the diode to allow it to store more charge (exposure) in the low gain state. More charge/signal is a better exposure/SNR.

But since "exposure" is charge vs capacity, disabling the secondary capacitor makes the photosite more sensitive to light (high gain state/higher base ISO). And this is more beneficial when you don't have enough light to saturate the larger capacity, because it increases the conversion gain for a given exposure. These are actually different levels/amounts of exposure; not gain. Basically, when you have a lot of light it makes the photosite larger by making it "deeper"; with all of the benefits larger photosites have. And it makes the photosite smaller when there is not as much light, which reduces the noise floor and improves the SNR. This changeover is typically hard coded at a given ISO, and not user selectable perse.

Note that the changeover point/ISO does not necessarily represent the difference in base sensitivity. I.e. my Z9 has ~ 1 stop less sensitivity (lower base ISO) when the secondary capacitor is active, because it ~ doubles the photosite's capacity; but the changeover occurs at ISO 500 (ISO 560 in auto ISO).

This drawing more accurately shows the dual ISO technology.

Dual gain as used in cinema cameras, and a few photography cameras (e.g. the Panasonic GH6), use both gain stages simultaneously when selected. They use the high gain stage for enhancement of shadow details, and the low gain stage for highlight details which do not need as much amplification. The high gain is additional amplification which also amplifies noise. This is most often considered/termed dynamic range expansion (or similar) and is typically user selectable.

Your dual gain diagram would be more accurate if the low gain was always on and the high gain was switchable (addable) in parallel like this.

The gain stage applied in both is analog amplification (gain); it is not conversion gain. Conversion gain is how much charge gained/collected by the diode equates to how much exposure. The dual ISO has switchable conversion gain; the dual gain has switchable analog gain.

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Edit to add:

Some video cameras switch between two gain stages (high/low) with fixed levels of amplification (e.g. Blackmagic Pocket 4k). They then use digital gain and gamma curves applied after the ADC to adjust the exposures further.

Aptina white paper on Dual ISO sensor design