How each class heals differently from each other in ESO *Updated for Scale Breaker

The vision of Elder Scrolls Online is to Play as you want. This is supported in game with offerings of in Skill adviser with a Build for each class. Still taking it a bit farther, I believe each class has something to offer. 

Elder Scrolls online offers many ways one can play any of it's offered classes, but I believe each class for healers has something unique to each other compared to other classes in that particular play style. As such first, I will mention Orthodox Healers which are most accepted healing classes in the game, while then going over the non traditional or Unorthodox Healers afterwards. 

Orthodox Healers 

Necromancer -  As noted by the developers this play style of healer will be more about positioning. Taking a look at the skills we notice that change effectiveness via position of allies or caster.
Warden - As noted by the developers this play style of healer is about rewarding players for good timing and prediction of skills. This play style is about timing skills to when allies take damage and protecting them with healing skills with things such as heal allies as they take damage.

Templar Healer - As noted by the developers this play style is about protecting the house. This class of healers uses skills to protect allies within it's field with various sets of skills.

Nightblade Healer - As they have a skill line of their own for healing there leaves no doubt they were build to do this role. In fact, besides Templar class they were the 2nd most recognized healers till wardens. In tradition they offered high healing over time and damage. With changes sometime last year, they offered less dps to split off very their dps counter parts, but in return got speed to give to allies while putting slow debuff on enimes. Now with Elsweyr they have options that offer more utility then templar counter parts. They have Major Fracture and Major Breech though can only be used on one target (also marks shows hidden enemies). Aoe Minor Vulnerability allows them to really give buffs to allies damage, though they share this buff with magicka and stamina dps depending on group compostion it could be asset, especially in smaller groups where the uptime won't be easily maintained. They also have snare immunity, and silence that gives them edge in pvp aspects as healers. They are only class with  major vitality and major protection which makes them one par with Warden and Templar utilities for support and ahead of necromancer. This along with ultimate generation gives and low cost ultimate gives this definite style. Issue with synergy need on healers is fixed with necromancer/warden offering 2 as healers or necro tank self synergizing. Now it's just a matter of testing them on and they will be official members of the orthodox healers. 

Unorthodox  Healers

Sorcerer - This play style is while recognized by the developers as existing with the skill adviser, it has lost some identity in how it compares to other healer classes since Murkmire changes. Grasping the potential of the class, I think it's key features of play style is flexibility. While lacking in traditional support, it has skills to adapt to teams and change the field for the benefit of the team. Some skills really could use some reworks (encase) and touch ups ( negate) though for this play styles really to shine for the community.

Dragon Knight Healer - I think of the all the Classes of healers these are the black Sheep of the developers right now. The play style is recognized with developers, but they have a lot of functionally issues. Still focusing on their play style, I see this play style as slowing down enemy assault. This is done by shields that protect allies from damage even before it happens and slow debuff on approaching enemies.