Gear, while it doesn't outright say it on it, seems to fall within the "plate, mail, leather, cloth" categories.

Plate: PLD, WAR
Mail: DRG
Leather: MNK, BRD
Cloth: WHM BLM SCH SMN

DRG and MNK have very similar stats, but different armor types. Allagan gear between them might look similar or even the same, but that doesn't mean it's the same armor type.