There's "support" which is somewhat different from healer, as Healers generally just keep the party alive and Support makes it so everyone else does their job better (either by buffing them or debuffing the enemy).

Thieves are damage dealers that just have the steal ability. They're more or less glass cannon types.

And another support would be Auron (Samurai) from FFX: he did pretty good damage but the real reason you wanted him in the party would be for his "Break" skills that lowered the enemy's defenses.