[simias]

That's not entirely accurate. It's true that a camera will capture the image during a certain interval of time instead of a definite point in time (obviously) but the length of that exposition time is not necessarily connected to the framerate.

For instance if you have a digital camera where you can select the framerate (pretty common these days) and if the exposition time was simply the frame period, it would mean that the image at 30fps would be exposed twice as long as 60fps and the resulting picture would look very differently.

Of course you can mitigate that by changing the aperture and other parameters but in my experience in practice you can select the exposition time and framerate independently on digital cameras. With very sensitive sensor and/or good lighting you can achieve very small exposition times, much smaller than the frame period. If you're filming something that moves and unless you want to be blurry on purpose you probably want to reduce the exposition time as much as possible in order to have a clean image, just like in the video games.

[stan_rogers]

...and it will look very awkward if there is motion in the frame if you're not shooting very close to 1/(2 * framerate). There is a very small tolerance window, outside of which the picture will look mushy (if your camera lets you shoot very close to 1/framerate) or jerky (< 1/(3 * framerate)). Controlling exposure, if you want to maintain a constant aperture for depth-of-field reasons, is done using neutral density filters (including "variable ND" crossed polarizers) and adjusting the sensitivity/gain/ISO, not shutter speed.