When a game has a set of scenarios, that differ from the general play elements (generic maps, player vs. player), it is very often referred to as a game's campaign. Not all games do feature such a thing. For instance, early Counter-Strike did not have any form of campaign.
Games that only feature a campaign may still be played in multi-player in form of a coop, if they have one. Some games do not feature that and are single-player strictly (Dungeons). On the other hand, there are single-player games, that feature no campaign but only a play against bots (Warlords 1). So a game having a single-player does not automatically mean, a campaign is available.
There are forms of pseudo-campaigns (such as Unreal Tournament 2004, where you basically only play multi-player maps against bots). Such games can be referred to as having a single-player but not really as having a campaign.
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