Which word is correct, empathic or empathetic?

That depends on the usage. If a person can feel or identify with the pain of another, they are empathic. If they understand the pain of another, they are empathetic. Empathy is the ability to feel or another's emotions as though they were your own. You can be empathic while feeling empathetic toward another. Its just a different verb tense. I empathize with your confusion, though.