What is the different?

Well ok, I may be wrong about Rising Sun, but I have read in several places that it works as a %.

However, about how absorb works, you don't have it quite right. What would happen in your example with the 12 lightning damage is that you immediately heal the 12 lightning damage and take none. Absorb IMMEDIATELY heals whatever the listed value is (be it a % or numeric value). That is why some people think that the first shard of Blizzard is bugged. If you have full life, all of your cold absorb immediately applies life to your bulb (which is already full - so you see no effect), then you take the rest of the damage straight up (minus what you absorbed, even though it didn't really add anything to your life).

So, in essence, absorb is like a double resistance. However, it only helps to its true effect if you already have life gone. That is why stacking lightning absorb against a trapper or cold absrob against a blizzard sorc doesn't always work as they can easily 1-hit KO you.

Does that make sense?