From what I have read all HSPs are not necessarily Empaths, but it's probably safe to say all Empaths are also HSPs.
I took the test here several years ago:
The Highly Sensitive Person and got one of her books.
Mostly I was just relived to see that the way I perceive things IS within the range of NORMAL. That, if I don't laugh at others being in pain, I'm not crazy. That is a normal reaction for an HSP.
Example, why are the "Three Stooges" perceived as funny with all the hitting they do? They are not funny to me. An HSP might say that.
I can think of other times in my life when the people I was with thought it was VERY funny to bully another, punch down, or make fun of the one in the group who just didn't understand what was going on. NONE of that was funny to me.
Then I come away from those workplaces or social gatherings thinking I'm Debbie Downer. No, I'm not Debbie Downer, but that bullying kind of "humor" is not funny to me. I think I just have a lot of empathy for the one being bullied.