I think its the runny honey thats treated. Unprocessed honey starts runny but will solidify after about a month. To keep it runny for longer it is heated to break down the crystal structure completely. If you can get honey from a beekeeper then you probably should, its much better and often cheaper too.
Ok, did a bit of hunting around, as it seems that there's a little misconception about what's what.
Now I'd have thought, that crystallised honey is just that. Honey that's been stored long enough for the crystallisation process to begin naturally. It would seem that there are also some honeys that will do this quicker than others i.e. Oil seed rape/Canola, is a honey that's famed for being a PITA and crystallising quickly, sometimes even still in the comb.
What's referred to as "set" honey is somewhat different. It's smooth in texture, not gritty like crystallised honey. It also seems that to produce the "set" honey, you'd take some that is already set and "seed" a batch of runny honey. This is then churned/stirred, to help it form more set honey, which it would seem, is just seeded then churned to help it start to crystallise, but with much finer crystals than honey that's solidified through age. It (the set stuff) has that smooth, almost butter like texture.
Which is what I'm trying to explain i.e. the difference between crystallised naturally, which is gritty and "set" honey which is "manufactured" to be solid yet smooth textured.
Ah ha! [ame="http://www.youtube.com/watch?v=kLGE-7n0_Ko"]I've found a clip[/ame] that explains it... Hopefully you'll be able to play it to see what I'm on about....