The most widely used current designs are video-based eye trackers. A camera focuses on one or both eyes and records their movement as the viewer looks at some kind of stimulus. Most modern eye-trackers use the center of the pupil and infrared / near-infrared non-collimated light to create corneal reflections (CR). The vector between the pupil center and the corneal reflections can be used to compute the point of regard on surface or the gaze direction. A simple calibration procedure of the individual is usually needed before using the eye tracker.
Both bright and dark pupil eye tracking require active illumination, or in other words, that they require a controlled light source to be pointed at the user. The big difference in the setup is where the light source(s) are placed, either right next to the camera, or farther from the camera.
EyeTech has pursued dark-pupil eye tracking, and has focused on using that technology.
Dark pupil eye tracking has been in use for over 40 years. In EyeTech's setup, two infrared light sources are placed a few inches on each side of a single camera to achieve the dark pupil eye tracking method. These two infrared light sources reflect off the cornea of the eye.
In demos at trade shows and use over the years, it has had better success across ethnicities and in more difficult lighting environments. Some demographics have a pupil that does not show up well with bright pupil eye tracking. Kind of like how some people easily have a red-eye effect in night time flash photography photos while other people rarely have a red eye effect, may be related.
And on a related side note, EyeTech has focused on remote eye tracking, instead of head mounted eye tracking, meaning that the eye trackers are placed away from the user instead of being mounted into a helmet or a pair of glasses.