Ft. Hood Geoids & Ellipsoids

The type of model used to describe the earth depends upon the requirements of the application and the level of detail required.

Geoid
The geoid is a model of the shape of an gravitational equi-potential surface (sea level). This is used for field work, since all surveying and geodetic measurements (including satellite measurements) are made relative to this surface. The geoid is irregularly shaped, due to variations in the earth's density and topography, and must be determined by actual measurement.
Ellipsoid
An ellipsoid, in the context of geodesy, is a mathematical model of the earth's shape. An ellipsoid is calculated by fitting an ellipsoid of revolution to the observed geoid shape. This may be done only within a region of interest, such as the continental United States, or may be done for the entire world, as is the case for WGS84.

So, at any given point on the earth's surface, there are two different reference surfaces to deal with, the geoid and the ellipsoid. Surveyors use the geoid (mean sea level), since that's what's relevant to their field work. Using the ellipsoid is simpler for dealing with data over large areas.