Empathy is the ability to relate to what a person is going through. If an individual is defining a person as a victim, then they are demonstrating very little empathy. That is stigma. It comes down to communication. People should never assume how a victim feels, but should talk with them, be there to support them, and remind them of their strength and ability to overcome. That is empathy.
The difference is quite simple, stigma is defining a victim by what has happened to them, empathy is being there for the victim and reminding them of their strength.