Excellent discussion above, but here is the math that helps put light sensitivity, focal length, aperture together. Remember the exposure triangle - shutter speed, aperture, and ISO, adjusting one, requires adjusting the other for the same "perfect" exposure - but different features such as resulting motion blur or different depth of field. With todays cameras, grainess of higher ISO is not as much a factor as the old film ISO, both native and push processing.
And here we go...!In addition, remember the exposure triangle as you need more light and you can't open the aperture further, so it is slower shutter or higher ISO.
No offense intended, I am sure you have only the best intentions with your explanations, but as they are fundamentally flawed they do not help overall.
No matter how many articles, webpages, YouTubers, and whatever else, may state it... there is NO "exposure triangle"! This is one of these everlasting misconceptions in photography, but no matter how often it gets repeated and how fiercely it gets defended... it´s simply false.
In most easy terms: The only elements that have direct (!) control over the exposure in your camera are aperture and shutter speed. ISO is NOT the sensitivity of your camera sensor (!), means it does not alter the sensitivity of the sensor when changed. ISO is a scaling coefficient applied to the data / signal obtained as a result of the exposure.
If of interest, potentially to say good-bye to this misconception, maybe read this article. I think it´s one of the better articles to understand why there is NO "exposure triangle", never has been.
The Unbearable Lightness of Mystic "Exposure" Triangle
We should begin by saying that the point of all of this is not just to criticize one of the most repeated photographic myths out there – that's just a tool, because an incorrect understanding of the way that exposure and ISO work, as well as their roles during the shooting process, leads to a...
www.fastrawviewer.com
Another interesting article, again just one of a lot of available articles, is this one about noise:
What's that noise? Part one: Shedding some light on the sources of noise
How would you react if you were told that the aperture and shutter speed you choose make more difference to image noise than the ISO setting? You might be surprised to discover that a lot of the noise in your images doesn't come from your camera at all: it comes from the light you're capturing...
www.dpreview.com
First when we understand these basics in photography we may subsequently understand other impacts like bigger sensors on aspects like low light capabilities, resulting noise in a final image, and so on.
Herbert