When using an eye tracker, it is most often the gaze that is of interest, i.e. what a person is looking at. However, a person does not see things as a point in space, but rather everything that falls within the direction of a vector starting in the eye of the person being eye tracked and ending when it hits an opaque object. We call this the gaze vector. (This is a simplification as it assumes you only see what is registered by the very center of the fovea. For a more detailed explanation about how the eye and human vision works, please refer to the section Eye tracking essentials on the main Tobii Pro website.)
The gaze origin is provided for the left and right eye individually and describes the position where the gaze vector starts. Three floating point values are used to describe the x, y and z coordinates respectively. For screen based eye trackers the position is always described in the User Coordinate System, and sometimes in the Track Box Coordinate System.
The gaze point is provided for the left and right eye individually and describes the position of the intersection between the Active Display Area plane and the line originating from the gaze origin with the same direction as the gaze vector. The coordinates for the gaze point are given as a 3D point in the User Coordinate System and as a normalized 2D point in the Active Display Coordinate System.
For HMD based eye trackers, there is no Active Display Area, and hence it's not possible to calculate a gaze point (as described above). Instead, the gaze is described by a (normalized) gaze vector. The gaze vector is provided for the left and right eye individually. The gaze vector originates from the gaze origin, which is described in the HMD Coordinate System.