During the quests they mention them as Arcana, which is the classification used in Tarot for the two major sets of cards. So definitely influences from Tarot, but the cards in the game, as mentioned in the Astro questline, are based on the constellations of Eorzea. I've only got 3 of them so far, but I can list them so far.
Bole is the Trunk of the World Tree and represents the First of the Seven Heavens, the Heaven of Earth. It was planted by the Matron (Nophica) and is Nurtured by the Keeper (Althyk) and it is the source from which all life is said to have sprung.
Balance is Azeyma and represents the Second Heaven, the Heaven of Fire. It is made prosperous by the Traders (Nald and Thal), but is kept in equilibrium by the Warden (Azeyma).
Spire is a great iron tower of spinning gears and taut springs, and represents the Third Heaven, the Heaven of Levin. The Spire was constructed by the Builder (Byrgot) and is constantly under attack by the Destroyer (Rhalgr), but his levin bolts only serve to power the tower.
Arrow is Llymlaen and represents the Fourth Heaven, the Heaven of Wind. It was created atop a lofty peak b the Wanderer, Oschon, who was guided by the Navigator, Llymlaen, just as the wind off of the Navigator's seas guides the Arrow fast and true.
Ewer is the Scholar's Vessel and represents the Fifth Heaven, the Heaven of Water. The Scholar's Vessel pours forth a mighty river that flows across the Fifth Heaven. The river contains all knowledge held in the past, present, and future, and contains the aether spun from Nymeia's loom, which is the aether that makes up magick. The Ewer points one toward truth.
Spear is Halone and represents the Sixth Heaven, the Heaven of Ice. It is the Heaven the Fury resides in within her palace that she carved with her spear from ice formed from moonbeams gathered by the Lover, Menphina.