Here is how I find it is being split up these days (for the most part):

 1. `Campaign` or `Story` mode
 2. `Multiplayer` mode
 3. `Multiplayer` mode

The thing about the "bots vs. AI" discussion is that, for the most part, they are both the "multiplayer" experience . . . the game mode focuses around multiple players playing against each other, either in teams or individually.  Whether or not those "players" are controlled by humans or the computer is simply a separate detail of the experience.

Of course, there are games that have broken this dynamic  . . . Brink, for example, was a single [primarily multiplayer] experience, that used a mix of human players and bots (based on player availability), and also followed a campaign story, as each round completed, but I wouldn't use those exceptions as guidance, unless they apply.   :)