ISO changes the analog gain and in a way yes, it does make it more sensitive to a certain range of brightness.

This is because the ADC (analog to digital converter) right after can only handle so many bits of data (like 12-16ish in consumer cameras). You want to “center” the data “spread” so when the “ends” get cut off, it’s not so bad. Adjusting the ISO moves this spread around. In addition, even if you had an infinite bitrate ADC, noise gets added between the gain circuit and the ADC so you want to raise the base signal above the “noise floor” before it gets to the ADC.

Gain is not great — it amplifies noise too. You want as low ISO as possible (lowest gain), but the goal is not actually to lower gain; your goal is to change the environment so you can use a lower gain. If you have the choice between keeping the lights off and using higher ISO versus turning on the lights and using a lower ISO, the latter will always have less noise.

Most photo cameras have one gain circuit that has to cover both dark and light scenes. Some cameras like a Sony FX line actually have two gain circuits connected to each photosite and you can choose, with one gain circuit optimized for darker scenes and the other optimized for brighter scenes. ARRI digital cinema line cameras have both and both are actually running at the same time (!).