Spheroid, Ellipsoid, and Geoid
Spheroid is a solid generated by rotating an ellipse about either the major or minor axis
Ellipsoid is a solid for which all plane sections through one axis are ellipses and through the other are ellipses or circles. If any two of the three axes of that ellipsoid are equal, the figure becomes a spheroid (ellipsoid of revolution). If all three are equal, it becomes a sphere.
Geoid is the equipotential gravity surface of the earth at mean sea level. At any point it is perpendicular to the direction of gravity.
Smith, James R., Introduction to Geodesy: The history and concepts of modern geodesy. John Wiley & Sons, 1997.