International Association of Geodesy SC3 Report (1999) states three tide systems;
1. Tide free- Here a geoid exists with all direct & indirect effects of the sun & moon are removed.
2. Zero-This geoid would exist if the permanent direct effects of the Sun and Moon are removed, but the indirect effect component related to the elastic deformation of the Earth is retained.
3. Mean - This geoid would exist with Sun and the Moon ( no permanent tidal effects are removed).
Tide-free elements of the Earth's gravity field are non-observable since we can't practically delete Moon and Sun to infinity and remove all direct and indirect effects due to that celestial bodies.
For solving the boundary-value problems of the potential theory we must have elements of the Earth's gravity field in the zero-tide system.