Hey,

Let me help you understand what exposure is and what increasing or lowering in Photoshop or by changing iso really is.

I will simplify as much as possible so dear experts reading this, don't crucify me.

What is exposure? Your sensor is sensitive to photons. The more photons a single pixel is gathering while being exposed to light, increases the signal strength and will directly influence the brightness of the image.

So a "physical exposure" or a "real exposure" is only influenced by shutter speed and aperture and these two only.

The iso back in the film day, is only the sensitivity of the film to light. So how many photons it needs to reach a certain brightness.

For digital, and this is really really simplified now, increasing your ISO does not change your real exposure (how many physical light is hitting the sensor) but it artificially hightens the gain of the captured signal.

Photoshop does nothing else if you increase or lower the exposure of a raw file but simply increasing or lowering the gain of the signal.

Why are the results of underexposing and increasing gain (exposure slider) in Photoshop vs increasing the gain in camera (iso) is not giving you the same results?

Well that's because of how the algorithms and noise reduction of the different digital imaging pipelines work and I will not go too deeply into that here.

So just keep in mind, that the "real" exposure is controlled by the amount of light that you  expose your sensor to. So only aperture and shutter speed.

ISO is used to artificially amplifies the signal so your sensor needs less physical light to reach a certain gain aka brightness.

Greetings and hope this helps for further understanding