Agreed. I see compassion as the understanding of pain occurring and taking action to alleviate it. I tend to see empathy and sympathy as passive while compassion is an active process that can be very empowering.
Too often, I think intended empathy and/or sympathy can devolve into pity. No alleviation of pain occurs for anyone.
I’ve read the Dalai Lama’s “Book of Joy” a year or so ago. It was there I think I remember reading similar discussion about compassion and our need to foster compassion to alleviate more pain in ourselves and those around us.