If I have ISO 100 speed film in a camera and choose to expose for ISO 400 speed film, I'm underexposing by two stops. It is true that ISO 400 film is more sensitive (and thus brighter) than ISO 100 film. But when I change my camera's ISO setting to '400' I'm not actually changing the film's sensitivity to ISO 400 - I've still got ISO 100 film loaded! What I am doing is reducing the amount of light the camera's meter says my film needs to be 'properly' exposed. So my film winds up underexposed by two stops.
In other words, the ISO setting for film cameras doesn't affect the sensitivity or 'speed' of the film at all. Rather, it affects the calibration of the camera's meter by telling it how sensitive the film that is loaded is.
When that film is developed, it needs to be pushed two stops brighter to get more or less 'proper' exposure. But the result will be lower contrast (brighter shadows) and coarser grain than if the film had been metered and exposed for ISO 100 and normally developed.
If you overexpose your film, you would normally pull process it by developing it for less time than normal. This will tend to increase contrast in the mid-tones and dark areas and muddy the shadows, but highlights that have been totally blown will not show detail, they'll just appear to be a uniform bright gray when printed.
The problem with changing the ISO setting while shooting a roll of film (unless you are thoughtfully using it as an exposure compensation control) is that the entire roll will almost certainly be developed for the same amount of time. Unless you're willing to skip every other frame when shooting, then fumble around in the dark and count sprocket holes by touch (without getting fingerprints on the actual exposed frames) in order to clip different parts of the film apart before developing it, the entire roll gets the same amount of development.
When you do a bit of both over and underexposing on the same roll and don't tell the film processors any differently, the film will be developed at box speed. When prints are made from the negatives, the machine that scans the film will usually automatically try to adjust for under/over exposure. Since most film has a pretty wide exposure latitude, in skilled hands the printing lab can usually pull decent results out of slightly over or underexposed negatives.