What is the difference between these healing perks?
I am unsure what the differences are between these sets 2-piece healing bonus perks on artefact sets. They looks identical to me, just with different wording.
Character Healing Effectiveness +15%
Healing Bonus +15%
What are different bonuses doing?
Should be exactly the same.
If you look at the artifact summary screen (don't mind the actual number, this is just a random screen I found on Google)
you should notice that in both cases the "Healing Bonus" parameter is increased by 15%. So this is just inconsistent wording.
Note that this is different from the 2p bonus on Traveling Doctor, which only increases the effect of received healing.