The following are my opinions entirely, influenced by what I learned and how I play the game:
WHM: In a glance, they seemed to be the on demand 'big bursty' of the healer siblings. Very reactive. Able to pile up lilies, amplify said burst heals, dump a massive burst of heals when needed (hello Cure III), and supplied by several other bursty nature abilities whether it's more healing (assize, lilybell), or damaging (assize again, and misery).
SCH: The 'resource maintenance, totem healer'. Packing a boon of mitigative potential but requires slightly more foresight to pull it off effectively. Based on their past iteration and current existence of Chain, it seemed like they're the more support-oriented of the healers, leaning toward debuff application & supporting their party defensively.
AST: "FASTro". Plays heavily to the aspect of a time magebecause you press so many times f*cking button in 15sthrough the use of delayed heals and (in the past) extension of buffs. They're also the support-oriented of the healer like SCH, but instead focusing more to amplify their allies' damage through the use of not-so-random cards. I often joke that this is your "Gacha Healer".
SGE: "Less thought-Weaker SCH", "Pseudo Barrier Healer". Wait.. for real though, Idk. There's just no real identity to this newest healer besides "hahaha space lazor oops I forgot Kardia exist." and "please take more damage I need mana."
MNK: (At least until they remove Greased Lightning) Felt like the "need for speed"-of the melees as opposed to strong, single attacks.
NIN: The 'debuffer' of the melees (Old Trick Attack R.I.P.).
SAM: The 'I build gauge to unleash ultimate finisher'-melee.
BLM: A turret with constant high output rather than bursty like the rest of the existing jobs saves healers. "I don't wanna move" is their motto.
PLD: The 'selfless, most support oriented' of 4 tanks. Being only recently reworked to put more emphasize on their spellbade action though, I'm not sure I want to call them having any 'constant sustained damage' as an identity anymore.
WAR: The 'berserker, self regen'-tank based on what I remembered reading from their older iterationsbut they accidentally made the arguably best 5th healer in the game.
DRK: The 'magic oriented'-tank that relish in hurting themselves (lmao half joke) to unleash more fury.
GNB: DPS in a tank's trench coat. The thrill seeker of the tanks. (Can I do my mini burst here and still execute my planned mits? Oh Oh... let me do my miniburst while I move the boss.... skiiillffulllyy... oh f### time to shoot myself on the head with Superbolide).
Can't say anything for the rest 'cause I either don't play them much or I'm just bad with them. Or both.