There are several different game types in Empire Earth. In single-player, there are developer-created campaigns which have historical story lines. You may also create your own scenarios (or download others' from the web) and play them.
Random map play is your normal versus play that dominates multi-player and is available in single-play against computer AI. Random map settings are variable to create many different styles of game-play.
There are also a handful of scenarios created for multi-player.