The main quest and tell about lore in this game. Rewards from Main Quest vary. Most are EXP and Zeny.
Side quests, but greatly affect the progress of your Adventure Handbook. Rewards from this quest are usually Emoji, Hairstyle, etc.
This quest is a recurring quest, often found in cities. Some examples of Daily Quest are like Quest Board, Monster Wave, Rift / Crack Fixing, etc.
This unique quest can be found in every city. The quest given by NPC bard is the level of difficulty above the Main Quest. For example like kill 300 certain monsters. Reward from bard Quest is Unlock Crafting Equipments in the city where Bard Quest is done. Also unlock like Fun Toys, Hairstyle, etc.
Headgear Quest is often found in cities. Reward from this quest is a recipe for Headgear which can later be drawn. Quests given by NPCs are often:
Kill Miniboss / MVP
Take photos of Miniboss / MVP killed
Give the rare material dropped by Miniboss / MVP.
Please check the following picture.
This quest is fairly easy. The reward for this quest is to open a photo spot location (read the Adventure Handbook page for photo spots).
Quest battle with NPC, the reward is Battle Token items which if used will get EXP and Job EXP.
This quest is only found when Base Lv. 60, first came out in Payon City. The rewards vary.
Quest that is only available at the Guild Hall. The reward is the Silver Badge which is used for guild purposes like Valhalla Ruin (Guild Raid).
Elite Bard Quest
Just like Bard Quest, but this quest has a level of difficulty above the usual Bard Quest.
Glast Heim Quest
This quest can only be found in Glast Heim. Rewards from this quest vary, if completed, you will get Costume Weapon at the end of the Glast Heim quest.