There is a difference between being able to show empathy for a person. It is good to be able to care about a person you know/meet and get to know them. It is great to have compassion for others. Having empathy for another person, peoples, race, situation etc but then when that person has gone from your mind then your emotions can easily be refocused.
For myself, being an empath is having that capacity turned up to a very high level. For me when I walk into a room at times I can sense the mood that is there and I find it so overwhelming. I can be in places where people are, say a supermarket, not even at the check out yet. and am totally freaked out and I cant stop other peoples emotions impacting me. I can be in one room and a person can be in another room and I can feel exactly what they are feeling and when they leave that room my emotions go back to normal. Nobody has to tell me stuff, i just feel like some emotional human sponge. I find it impossible to know what my emotions are at times because the other persons emotions have moved in over mine . I cant separate where things are comings from. I cannot watch news shows. They weigh me down. I often feel heart sick from things in the world that I just have to hide away from every thing and everyone. It is so hard to refocus.
I had never heard the word Empath until the last couple of years but everything fits. Some people think it is wonderful. The pain I feel from it is a curse.
Sister Rags - I am untrained and a sponge and have not learnt any skill about this. But I just found this one the web and it helped me so I hope it helps you too.
Being Empathic versus Being an Empath: Crucial Differences