What is the difference between empathy and compassion?

Some of our users are interested in the difference between empathy and compassion. Compassion is the broader word: it refers to both an understanding of another’s pain and the desire to somehow mitigate that pain:

Our rationalizations for lying (or withholding the truth)—"to protect her," "he could never handle it”—come more out of cowardice than compassion.
— Eric Utne, Utne Reader, November/December 1992

Sometimes compassion is used to refer broadly to sympathetic understanding:

Nevertheless, when Robert Paxton's "Vichy France" appeared in a French translation in 1973, his stark and devastating description ... was rather badly received in France, where many critics accused this scrupulous and thoughtful young historian either of misinterpreting the Vichy leaders' motives or of lacking compassion.
— Stanley Hoffmann, The New York Times Book Review, 1 Nov. 1981

Empathy refers to the ability to relate to another person’s pain vicariously, as if one has experienced that pain themselves:

For instance, people who are highly egoistic and presumably lacking in empathy keep their own welfare paramount in making moral decisions like how or whether to help the poor.
— Daniel Goleman, The New York Times, 28 Mar. 1989

"The man thought all this talk was fine, but he was more concerned with just getting water. And, if I was going to be successful on this mission, I had to remember what his priorities were. The quality you need most in United Nations peacekeeping is empathy."
— Geordie Elms, quoted in MHQ: The Quarterly Journal of Military History, Autumn 1992

In some cases, compassion refers to both a feeling and the action that stems from that feeling:

Compassion, tenderness, patience, responsibility, kindness, and honesty are actions that elicit similar responses from others.
— Jane Smiley, Harper’s, June 2000

while empathy tends to be used just for a feeling:

She is also autistic, a disability that she argues allows her a special empathy with nonhuman creatures.
— Tim Flannery, The New York Review of Books, 29 April 2009