To give you a couple of simple differences...won't get to complicated here.
1. Scholar used more preventative healing with its shields and has really weaker AOE healing (got a bit better in the expansion with Indomitability though). But can do some really good dps. The fairies can be controlled or left to their own (better to control them for serious content). Scholar by far is my favorite of the three healers so far but I have not got my Astrologian to 60 yet so take that with a grain of salt.
2. White Mage is the best pure healer with great single target and AOE healing capabilities. White mages can do great dps also...don't get me wrong.