I think there's something wrong with the claps when I access medium via my hp. It keeps bouncing me out from the article.
Anyway, I was taught in school the difference between sympathy and empathy is whether we experienced the ordeal before. If we did, we knew how it felt like thus it would be known as empathy.
I like the way you described these three words especially when it comes to compassion. Now I understood better what compassion means.