I've asked some other questions that are very complex, and breaking them apart I'm concerned with how a geoid is represented. I see some people refer to it as a grid, and others refer to it as if it was not a grid.
Going on the EGM2008 WGS84,
Those wishing to use EGM2008 to compute geoid undulation values with respect to WGS 84, may do so using the self-contained suite of coefficient files, FORTRAN software, and pre-computed geoid grids provided on this web page. For other applications, the previous release of the full 'Geoscience' package for EGM2008 can be accessed through the link at the bottom of this web page.
So there is a "pre-computed grid" that they distribute. I believe some people are calling this The Geoid.
EGM2008 is a spherical harmonic model of the Earth's gravitational potential, developed by a least squares combination of the ITG-GRACE03S gravitational model and its associated error covariance matrix, with the gravitational information obtained from a global set of area-mean free-air gravity anomalies defined on a 5 arc-minute equiangular grid. This grid was formed by merging terrestrial, altimetry-derived, and airborne gravity data. Over areas where only lower resolution gravity data were available, their spectral content was supplemented with gravitational information implied by the topography.
So EGM2008 "The Geoid" is a model of gravitational force from a bunch of merged stuff.
So it seems, in short, EGM2008 is a fancy gravitational model that is reduced to a pre-computed undulation grid of 1x1 Minute, and 2.5x2.5 Minute.