Sea of Thieves will not follow a typical storyline. The game won't have an overarching linear plot. However, it will feature smaller stories that can be completed during a playthrough. They will be narrative and follow similar quest styles from previous adventure games.
In addition to standard quests, procedurally generated quests will also be present. Looking for sunken ships, buried treasures, and other objects may take you off course and into unfamiliar territory!
Voyages are considered to be Quests in longform. These will take significantly longer than a quest.