There are three things that affect the overall exposure of your image (how light or dark the image turns out): shutter speed, aperture and film speed (ISO).

This question What is the exposure triangle? covers the relationship of those three very well, so suggest you read that. But basically if you have some combination of those three settings which results in a good, well exposed image, and then you change one of the settings, you need to change one or both of the other settings to compensate.

The film speed, or ISO, tells how sensitive the film is to light. Lower ISO numbers like 100 are films less sensitive to light. Higher ISO ratings like 400 or 800 are more sensitive to light, so they require less light to expose the film. Meaning you can have a smaller aperture (lens opening) or you can speed up the shutter, because your faster film needs less light.

So if you keep the aperture fixed, then as you increase the film speed, you can also increase the shutter speed (more sensitive to light, so need less time to expose).

But if you increase the film speed and use a smaller aperture, you could leave the shutter speed alone.

So they do affect each other, but just not in lock step because you have that third adjustment of aperture which also comes into play.