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.
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.
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 at 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.
Nightshade Healer - Unlike Dragon Knight and Sorcerer, developers had always given them ability as healers and besides Templar class then were the 2nd most recognized healers. 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. This along with ultimate generation gives and low cost ultimate gives this definite style. If not for their issues, with healing large groups (aka trials) and ongoing synergy issue in combat for healers, then they would still be recognized as a popular choice for healers as they were three years ago.
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.