What are the real differences?
Here is a couple of random thoughts that stroke me along the way.
First, you cannot AFK as a healer: you need to always be looking at your screen, this is the end of semi afking during trash. You as a healer is the person that should never lag/DC or whatnot.
Second is judgment, as a DPS the only judgment you need is enough intellect to not pull from the tank (although quite hard these days)or not break CC, as a healer you will more than often need to assess very quickly whats going on and heal the right person first (usually it ends up by either you or the tank). But the usual rule does not always apply (applies only in 5men in fact), in a raid everything is different, for example as a paladin, i usually choose to not heal myself (Spiritual Attunement will give me mana back).
As a healer I can decide where I am going ... there is always a spot for a healer ... as a DPS it's more problematic to find !
As a healer I get a lot of whispers to be invited to groups for Heroics/Raids ... even if it's happening on my hunter because people know me ... it is not THAT often !
And remember:
When the tank dies it's the healer's fault, when the healer dies it's the tank's fault, when a DPS dies ... we told you to stay out of the fire ;-)