From what I understand about the class system, you can't look at the callings of the characters, but rather at the active soul the character is using.
for instance, clerics can choose from 8 of the following souls: sentinel, warden, justicar, cabalist, purifier, shaman, inquisitor, druid. From those 8 classes the sentinel, warden and purifier are the healing classes, justicar is the tank class, shaman and druid are melee dps, the inquisitor and cabalist are ranged magic dps.
The shaman and druid are straight up dps classes, but don't have any party heals, save for some selfheals, and the druid has a small pet who heals the druid and the party by a little. Justicar is mainly tanking, but has a skill that enables him to heal the party everytime he hits like you said, the inquisitor and cabalist from what I've heard aren't able to heal aswell. The benefit from being a melee dps cleric soul, is that when needed you can switch to one of the healing classes on the fly using roles. And each character can have up to 4 roles.
I also picked up that in the mage souls, the Chloromancer is a healing soul, and in the Rogue calling there is a soul able to tank aswell.
Basicly each of the 4 set callings have their archetype: Warriors tank, clerics heal, rogues stealth, mages glasscanon, BUT this is what I like about rift, if you decide you wanna dps as a cleric, you don't have to reroll, just switch out some souls and voila, you are a full dpser. Same for warriors, tired of tanking, no problem, click of a button, they can now dps.
As a conclusion, don't call all clerics just clerics, name each class by their souls. For tanking alone, there are about 5 souls total I believe divided between cleric, warrior and rogue.