Class vs job?

[Enkidoh]

The difference between the two mostly stems from the fact that classes are Disciplines currently taught by Guilds with a regimented structure. Jobs on the other hand, are Disciplines from earlier eras that either fell out of use and were forgotten due to their practioners dying out (SMN, SCH, MNK), either the Job or their skills are strictly controlled due to their practioners being exclusive or secretive (DRG, BRD, PLD, RDM, DRK), are from foreign lands or are not native to Eorzea (AST, WAR, GNB, NIN, SAM, DNC) or have even been made outright illegal (BLM, WHM). And some have been made literally out of whole cloth then and there (MCH, BLU).

Hence why Jobs use soul crystals, they're something of a shortcut to mastering their skills quickly rather than using the more 'traditional' Guild-based teaching system classes use. They effectively serve as a conduit for memories of past practioners of that Job, allowing you to draw on those skills while also simultaneously recording your own memories into it (MCH and BLU's ones are literal blank slates though so you're basically winging it with those).

That's the basics of the lore for them as I understand it anyway.