Digital cameras use either "global" or "rolling" virtual shutters. "Global", as described in this article, is just a perfect "all pixels start and stop capturing light at the same time". This is more expensive to make because you need to have extra circuitry and memory on the sensor to read out the value of all sensor pixels more or less simultaneously.
"Rolling" is where the sensor rows are exposed then read out one at a time in sequence, from top to bottom. This is cheaper to make because you only need to be able to read out one row at a time, so fewer A/D converters on board, less memory, etc. This is roughly equivalent to having a "shutter" with a thin horizontal slit that slides from the top to the bottom of the sensor quickly on a film camera. It does what you might imagine to fast-moving objects, distorting them so they are slanted, squashed, or stretched.
There's actually a third secret mode some budget digital cameras use called "global reset release". These are rolling shutter cameras that are setup to start exposing all the rows in the image at once, then read them out as quickly as it can. This means that the rows at the bottom of the image keep collecting light while the top of the image reads out, meaning the image gets brighter and blurrier as you get towards the bottom. However, if you include a mechanical shutter and snap it closed once the desired exposure time has elapsed, the sensor can take its time reading out the rows one-by-one while the shutter protects the still-active sensor from capturing more light. Its a neat idea, but it greatly increases the time between shots so it's not too popular.