How are EGM96 and WGS84 related to each other?

Ian's answer is incorrect.

WGS84 approximates Earth by an elipsoid, which is basically a deformed sphere. EGM96 is a more complex model based on the gravitational force of the Earth (which is not constant) that defines what "sea level" or "up/down" mean, a smooth but irregular shape called "geoid". WGS84 is the elipsoid that best fits that geoid, and this fit has been updated as more accurate measurements of the geoid have been carried out over the years. WGS84 is not outdated; it's just a simplified mathematical model used by positioning systems like GPS, even if a geoid is technically more accurate when it comes to define the height over the sea level (since this is different from GPS altitude). You just have to translate coordinates when you need such distinction.