FFXIV Common Icons Guide Part 1

No matter you are beginners or skilled players of Final Fantasy XIV, perhaps you can't recognize all of the icons in game. However, if you want to show how experienced as a FFXIV player or play game easily, you'd better to have a basic understanding of common icons seen in the game. This is a overview of FFXIV common icons for both beginners and skilled players.

Disciple of War/Magic Job Icons

Disciple of Land/Hand Class Icons

Pet Icons

Quests
Quest Types

Quest Icons

Secondary Quest Icons

Gold Saucer / Triple Triad Icons

FATE Icons
The different sets are just used in different windows, locations, etc inside the game. They're all meant to portray the same thing (they're all meant to show the job or class that is their icon.) There's no super special 'meaning' behind any of them.
For the 'class' listing at the top: Set 1 is usually seen on signs or buildings in the towns that the guilds are located in. Set 3 is what you see on the 'Duty Status' window when you're waiting in the Duty Finder queue. Set 5 is seen in the 'Search Info' for people. etc..
For the 'job' list up above, the first set was used more in 1.x than it has been in A Realm Reborn, which is why Ninja, Summoner, Scholar, and Arcanist don't have that colored icon. Because it doesn't exist/the icon was never made because those classes/jobs didn't exist during 1.x.
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