The campaign is a series of eight levels that tell the story centered around a crusade. You can play the campaign on easy, medium, or hard difficulty. The campaign is a good place to start playing if you have never played the Anno series before, since it guides you through some of the basics of playing. Campaign levels tend to be the quickest to win, although each level can take several hours or more to complete.
There are six scenarios that you can play as well, each having specific objectives. Two are rated easy, two medium, and two hard. You cannot change the difficulty. The scenarios can take upwards of 20 hours each to complete, as long or longer than a continuous game.
Venice adds 15 new scenarios. They range from short, adventure missions to more complex warfare and building missions. There are also new medals and achievements for these quests.
A continuous game is a free-form game where you can set all of the parameters for the game, such as AI opponents and victory conditions. You can also set no victory conditions, which makes the game truly continuous. A continuous game with no opponents is a good place to learn the mechanics of the game. A continuous game is also very useful when trying to complete certain achievements since you can customize many settings, and some achievements can only be attained during continuous mode.
The quests page contains information about the numerous random quests that appear in the scenarios and continuous games. Note that no random quests appear in the campaign since all campaign quests are static, one-time-only quests.