For me at least, coming from the single player titles, the job identities can be found quite well if you just take a look at the current pvp iterations as they are reflected extremely well there instead of the watered down and restricted by encounter design of the PvE skillsets:

PLD: Protecting allies at its main core with holy magicks and high support skills (think FF4 Cecil)
WAR: Reckless wild fighting style at the cost of their own health which is offset by their high vitality and counters (see FFX-2s Berserker)
DRK: Sacrificing own HP to boost attacks while boasting incredible defensive capabilities (Dark Knight Cecil comes to mind)
GNB: Highly agile swordsman that draws enemies magicks to junction to themselves to increase stats and gain new abilities (aka FF8 Squall)

WHM: Simple but powerful healer archtype with a wide array of healing, buffs and strong holy spells alike
SCH: Scan and exploit enemy weaknesses while using their unique toolkit to deal with any situation
AST: Using the power of stars to predict attacks and use buffs like haste to manipulate time (Oracle/Time Mage hybrid)
SGE: One that blends the highest level attack and support magicks while also having unique spells (probably the one that deviates the most from classic FF sages)

BRD: The ultimate buffing archetype
MCH: Has a toolkit for every occasion while also dealing massive damage (mostly modeled after FF6's Edgar and his OP skills)
DNC: This one has traditionally been the counterpart of Bard, being a debuff specialist but turned into a buffer here, making it closer to the Songstress of FFX-2)

BLM: Raw destructive powerful elemental spells (fire side) with a wide array of disruptive spells (blizzard side)
SMN: Summoning divine beasts to deal massive damage in a large area (LB) while also drawing upon those said beasts (think FF9's Garnet)
RDM: Jack of all trades with usable melee attacks and a blend of lower white/black magicks at the same time. Dual cast as their signature trait

DRG: Uses their signature jumps to evade aoes and deal devastating damage from the back row
MNK: Gets close and personal with a flurry of fast attacks while also being able to take a few hits or even heal themselves with Chakra
SAM: Deadly katana wielders that target enemy weaknesses, usually taking them out in a few and swift hits. Often uses Gil in some way or another (see FFX's Yoooojimbo)
RPR: Rarely a playable class, a lot of bosses used to wield scythes but most notably FFT-0 Sice that turns the remains of their slain enemies into power
NIN: Stealthy high evasion dps that usually throws weapons like Shuriken and elemental veils for unique elemental coverage

I think out of all of the jobs - Sage, Dancer and Astrologian deviate the most from their classic FF job identity but not all that much to make them unrecognizable
As far as PvE goes... Ninja still does quite well with their mudra system, Red Mage is really on point and now Summoners match the job aesthetics really well