SCH is just healer summoner, Seraph is their Ultimate summon, similar to how Bahamut is with SMN.
Its LB has always been Angel Feathers, while WHM got the generic LB (Aerith's) that used to belong to all healers.

Seraph is an actual healing FF summon from VI and not just from FFXIV, imo it makes sense that their "trance" would be their Ultimate summon, like how SMN grows Bahamut wings on LB.

The job that struggles with its identity is WHM, with the nature theme being overwritten by the holy theme. The job quests are all about WHM being powers bestowed by the elementals. And its relation to nature. But it lost that identity with ShB sadly.

They're tacticians but the core of the job was always the bond of the SCH with their fairies, the quests have the fairy accompany you to save her previous summoner, you only do tactics in the ACN quest. SCH quests are about saving the cursed owner of the fairy.