Agreed, Scholars actually play more like Regen healers when playing them optimally. Majority of their regens are from the faerie (Whispering Dawn being their AoE active regen and Fey Union, Embrace, and Serpahic Veil acts as a passive regen) while they themselves have one at lv 80 (Sacred Soil). As a Scholar, you don't want your team to drop too low that your regens can't keep up, so you would use Indomitability or Consolation for AoE healing or Excogitation to keep people above a certain HP threshold. This is because Scholar's raw GCD healing is much weaker in comparison.
Meanwhile, White Mages excels in burst healing. They have a lot of strong single target heals (Afflatus Solace, Tetragammaton, Benediction) and can do good AoE Healing with Plenary Indulgence and Cure III.
To play optimally on White Mages, they use Regen as opposed to Afflatus Solace until 74 because Afflatus Solace heals 700 potency while Regen total heal over time potency is 1200. The net gain in 500 heal potency can be used to throw in a couple more damage spells instead. Throw in a Tetragammaton or Benediction, and usually this is enough unless you really need a burst heal, which would be the only time you would use Afflatus Solace. The same goes for Medica II until lv 76 when they learn Afflatus Rapture because Plenary Indulgence + Afflatus Rapture is generally enough for AoE Healing. After they learn Afflatus Misery (lv 74), White Mages rather keep everyone under a certain amount of HP so they can fully utilize Afflatus Solace's heal or Afflatus Rapture's AoE heal as they can both be used for movement due to being instant cast spells and can pay back some of the cost to use as a DPS tool in Afflatus Misery. At this point, Medica II and Regen are more like safety net skills. They are still very potent for healing purposes, but they don't give back DPS, so they take a backseat when trying to contribute more to the party besides just heals.