Quest

The main content in the game is quests. There are a variety of quests available - some are limited time only and some are permanent.

Story - quests related to the main stories of units in the game

 * Main Story - the primary story and typically what people mean when they refer to story quests. These quests also unlock the hard quests that are used to farm most unit shards. These quests are all permanently available and new story quests are periodically released.
 * Character Story - these are quests that expand upon the story of certain units (primarily 5 star units, but there are a few 4 star units.) Completing the level 80 character story for the unit will unlock a special master ability. These quests are all permanently available and new character stories are periodically released.
 * Babel Chronicles - a set of side stories relating to some of the unit homelands. These quests also unlock soul shard farming quests for a few of the units featured in these stories. These quests are all permanently available except for the hard versions of the quests, which provide job+ upgrades for Yomi, Sophia and Courage (these return periodically). No new Babel Chronicles story quests are expected to be released and all soul shards quests have been released for units associated with it.
 * Sacred Stone Memories - a set of side stories relating to a subset of units introduced via these stories. These quests are all permanently available and no new quests are expected to be released (except side stories which are located in events).
 * Genesis Story (Godless Revolution) - a set of side stories (in the form of a box event) relating to a subset of units introduced via these stories. These quests are temporary and return periodically.

Event - quests that provide a variety of alternative content and daily farming options

 * Current Events - this section contains mostly temporary events, but a few are permanently available. Each quest will have a duration listed for it.
 * Event Archives - this section contains events which have run previously and have been archived - most provide job upgrades, free units or farmable gear. You can unlock one quest a day for free in here. On occasion new quests are added to the archive.
 * Key Quests - this section contains quests that require keys to unlock. The keys are acquired through a variety of means depending on the quest. New quests for Babel War Arts are periodically added here.
 * Daily Quests - this section primarily contains permanent farming quests for items such as evolution materials, job tokens, enchanted job equipment, zeni, apples, ore, alchemia pots and gear shards/summon tickets. Occasionally there are special event quests that are meant to be done daily added temporarily to this section such as Consecrated Elements.
 * Special Quests - this section primarily contains side stories (in the form of a box event) relating to a subset of units introduced via these stories and existing stories/side stories. These quests are temporary and return periodically.
 * Collaboration Quests - can be found under Current Events and are limited time only. For the most part they are single run events with the exception of Phantom of the Alchemist.

Trials - special quests with non-standard mechanics

 * Babel Tower - this section contains tower quests, where you clear floors in order to get rewards. Note that all the tower events are only available periodically.
 * Shadow Plane Karma - this section has high difficulty quests for obtaining the free units Lil' Ouroboros and Waginau and their respective gear. These quests are permanently available.

Multiplay - quest you can do with other players
Typically they are quests that are multiplayer versions of standard quests, but there are a few quests that are only available in multiplayer mode.

Raids - occasionally available for a short period (typically 1-3 weeks.)
When available there will be a button on the home screen for the raid. Raids involve killing high health bosses for rewards and you can get assistance from other players in killing them.

Job+ and Job Enchantment - quests related to improving a units pre-existing job
These quests upgrade an existing job for various units. Job+ quests come from a variety of story, event and multiplay quests. Some are only available for a limited time during a seasonal event or box event, while others are permanently available through event archives, story milestones and multiplay. Job Enchantment materials are permanently available via daily quests (Enchanted Quest and the various JE quests that drop equipment diagram shards for a certain job.)