Shutter speed, ISO, and Aperture in photography are related in much the same way as Voltage, Current, and Resistance.
To change any of those three (in your case shutter speed) you have to compensate in one or both of the others. Lens aperture is limited mainly by form-factor (can't have a large aperture in a tiny zoom lens) and is therefore rather constant across Point-and-Shoot cameras. but Sensitivity can be improved by having higher-quality sensors and supporting circuitry.
My first P&S camera had a maximum ISO of 400 and was very noisy at that level. my first DSLR did 1600 (4x as sensitive) and the current bleeding edge is 128000 (8x more sensitive again). Even in inexpensive point and shoot maximum ISO seems to be around 1600 (or more).