Main Quest
The main quest and tells about lore in this game. Reward from Main Quest varies. Most are EXP and Zeny.
Sub Quest
Side quest, but it greatly affects the progress of your Adventure Handbook. Reward from this quest is usually Emoji, Hairstyle, etc.
Daily Quest
This quest is a recurring quest, often found in cities. Some examples of Daily Quest are like the Quest Board, Monster Wave, Rift / Crack Fixing, etc.
Bard Quest
This unique quest can be found in every city. The quest given by Bard NPC was the level of fitness above the Main Quest. Examples like kill 300 certain monsters. Reward from Quest bard is Unlock Crafting Equipments in the city where Bard Quest is done. Also unlock like Fun Toys, Hairstyle, etc.
Headgear Quest
Headgear Quest is often found in cities. Reward from this quest is a Headgear recipe that can later be crafted. Quests given by NPCs are often:
Kill Miniboss / MVP
Photo Quest
This quest is fairly easy. The reward for this quest is to open a photo spot location (read the Adventure Handbook page for spot photos).
Battle Quest
Quest battle with NPC, the reward is Battle Token item which if used will get EXP and Job EXP.
Elite Quest
This quest is only found when Base Lv. 60, first time out in Payon City. The rewards vary.
Guild Quest
The Quest is only available at the Guild Hall. The rewards are the Silver Badge used for guild purposes such as the Valhalla Ruin (Guild Raid).
Elite Bard Quest
Just like Bard Quest, but this difficulty level is above the usual Bard Quest.
Glast Heim Quest
This quest can only be found at Glast Heim. Reward from this quest varies, if completed it will get a Costume Weapon at the end of the Glast Heim quest.
In the quest list, you might accidentally find a quest with a red "X" as shown. Actually this is not a quest, but a tracker item. You can access it through inventory and choose an item. By using this feature you can monitor where you can get items, and how many items you now have.
After you understand using the Item Tracker, you can use this trick to find items that are not in your Inventory. Go to Market, then find the item you want to get in the Market. After that, use Item Tracker so you can find out where the item came from.