The tradeoff is indeed the same in both film and digital photography. In film photography, a higher ISO speed means a larger film grain. The larger the film grain, the greater the chance that any given grain will be hit by a photon, thus increasing its light sensitivity while decreasing its resolution.

In digital terms, a higher ISO speed means that more sensor elements (which are thus more likely to catch that photon) are used to determine the lightness value of a single pixel -- but, that pixel must then be larger. For example, if you had a 100x100 sensor array at ISO 100, your image would be 100x100 pixels. However, at ISO 200, four sensor elements would be used for each pixel, and you would effectively have a 50x50 pixel image. At ISO 400, 8 elements per pixel, and an effective 25x25 pixel image.

By the way, this is more of a limitation of the properties of light, rather than the properties of film & digital sensors. In the brief period of time that the shutter is open, you'll only get so many photons entering the lense -- which is purely a function of the aperature of the camera. For this reason, smaller sensors (which require a smaller aperature) are ALWAYS less light-sensitive than larger sensors, regardless of their resolution. Recently I've been looking at some high-end digital cameras (specifically the Cannon D60 -- drool...), and one of the nice things about them is that they have a larger sensor size, even if they don't have any increased resolution. That allows for FAR more light sensitivity, which can be more important than resolution in many contexts.

Cheers,

Nathan.