The Wikipedia article is out of date. The current WGS84 geoid model is EGM2008 which comes in two public versions: 2.5' x 2.5' and 1' x 1'.
WGS84 itself has has several realizations such as G973 and the latest, G1762, which are linked to various International Terrestrial Reference Frames (ITRF). Confluence GIS has a nice table on them. With each new realization, the latitude, longitude and ellipsoidal height values are little more accurate, and more closely match the corresponding ITRF to the point where they're matching within centimeters if not better in some places.
The EGM geoid models contain the difference between ellipsoidal heights (usually 'h') and geoidal heights ('H'). The differences are also called the geoid undulations ('N'). Thus you can use the model to convert between the two heights. Geoidal height is close to an actual elevation, and reflects how fluids would respond to gravity. When using ellipsoidal heights, water can flow uphill.
The geoid models are not accurate, not precise enough for the differences between the different WGS84 realizations to matter. The best, public geoid model available still has grid spacing of 1 by 1 minute. At the equator, 1' is around 1.855 kilometers.
If you knew you had EGM84-derived geoidal heights, you might want to convert back to ellipsoidal heights using the EGM84 model, then use a EGM2008 model to convert back again, but not much data that would have used EGM84 is accurate enough to bother doing that.
So far EPSG (IOGP's geodesy subcommittee) has only had one version of WGS84, although using 3 different coordinate systems (axes/units): 4326 (geographic 2D, lat-lon), 4979 (geographic 3D, lat-lon-h), and 4978 (geocentric, XYZ). The subcommittee just agreed that they would add the different WGS84 realizations, but only using the latter two coordinate systems (geographic 3D and geocentric). The information's been created, but still needs to be QA/QCed and released (as of October 2016). I don't have a timeline on that. Source: me, as a member of the subcommittee.