Compassion is not empathy, nor is it sympathy
I believe everyone has heard of compassion before. How much do we know what compassion is? If I ask you to explain what compassion is, would you be able to? Etymologically, compassion comes from the latin word compati. It can be broken down to com, which means "with, together" , and pati , which means "to suffer". Hence, in the dictionary, it means to suffer together with, or a strong feeling of sympathy and sadness for other people’s suffering or bad luck and a desire to help. However, based on this, how is this different from empathy plus the desire to help? In actual fact, compassion is much deeper than what the definition seems.
Some people may mistake compassion with empathy, sympathy, pity, or kindness. However, they are very much different. What empathy, sympathy, and pity have in common is that there is a person in front of them who is suffering. Someone with sympathy might say "I'm sorry that you are suffering". The emotional sorrow and sadness is there in sympathy. In empathy, you "feel" the other person's suffering. I used quotation marks here because it is not necessarily the other person's feelings.
Let me tell you my story. I will cut it short to cut to the chase. Someone I knew set me up and almost got me expelled. During the time I was suspended from graduation, I knew I had to conduct repentance, which I did. That was all in my mind at that time. I did not care about what other people are saying, or what else is going on. All I knew, was that only repentance will guide me through this ordeal. Naturally, this quenched my suffering. I wasn't suffering then. However, people around me started feeling sad, depressed, and angry, as they try to empathize with me on my suffering. However, have they really empathize with me? Or have they empathize with what their notion of me? That is why I used "fee" instead of feel. Most of the time we think that others are feeling something, but most of the time, it is our imagination.
Let's go straight to compassion. What then, is compassion? To say that compassion is the "to suffer with" is incomplete. In Buddhism, compassion is loving-kindness for all sentient beings, and the vow to relieve all forms of suffering from all sentient beings, and vowing that they will all become Buddhas. This is as extensive as I can go, if I were to summarize what compassion is in a sentence. If I were to talk in more detail, compassion is the second Brahmaviharas out of the four (loving-kindness, compassion, joy, equanimity).
When we inspect closer, compassion is the vow to relieve all forms of suffering from all sentient beings. But first, why would you want to do that? How do you generate that vow, or wish? It is because you have loving-kindness, the kindness that is universal across all beings, space, and time. Without loving-kindness as the causal ground, there is not compassion as the action. To say it in another way, to know that Enlightenment is marvelous, and wish that all sentient beings attain enlightenment is loving-kindness. To add on, without knowledge and wisdom of the Buddha, you wouldn't know what Enlightenment is, and wouldn't know be able to give rise to loving-kindness. It is the same for joy, which is the Dharma joy from seeing sentient beings being free from suffering.
Hence to talk about compassion without loving-kindness, joy, and equanimity altogether is akin to walking to a destination without legs, hands, or eyes. So, this is only a glimpse of what compassion is. To practice true compassion, one has to also practice loving-kindness, joy, and equanimity. How to we practice them? Contemplation on these four qualities.