Within the geodetic community, a geoid is a equipotential surface that roughly matches mean sea level if there was no topography.
You might want to take a look at this IERS site on the difference between ITRS and ITRF. ITRS, International Terrestrial Reference System, is the theoretical world system, which is then realized using a set of control points into an International Coordinate Reference Frame. They are always in ECEF (3D Cartesian), and in fact only acquire a particular ellipsoid like GRS80 when you need to convert the XYZ coordinates into latitude-longitude-ellipsoidal height values.
So back to your question. I would probably not use datum nor geodetic datum, but instead reference frame.