The words “sympathy” and “empathy” began their nascent existence in Classical Greece, and as you might expect based on that alone, their disparity is wholly philosophical and a little on the subtle side.
Sympathy originates from Greek “sumpatheia”, stemming from “sun” and “pathos”. This literally translates to “with feeling”.
Empathy, on the other hand, shares “pathos” but replaces the prefix with “em”, meaning “in”, to create “empatheia”, or, “in feeling”.
This is logical as empathy is the ability to understand someone’s situation, typically from first-hand experience or exposure – “in feeling”. Whereas sympathy is a little more detached, which means to have pity, sorrow or concern for someone, yet not necessarily true understanding of what they’re experiencing.
“Sympathy” reaches us in English through a string of Latinate languages, from Greek into Latin “sympathīa“, from Latin into Middle French “sympathie” and finally, by the late 16th Century, into “sympathy” that we use today.
“Empathy”, however, doesn’t seem to have been an English word until the late-19th or early-20th Century (first printed in 1909). This coincides with the theory of “Einfühlung“, first printed in 1873, which was a German term that expanded on the definition of “empathy” to include feelings towards the world around them in addition to human emotion, most notably at the time, this was applied to artwork and literature.
Equally, we gain “apathy” (“apatheia” – “without feeling”) and “antipathy” (“antipatheia” – “against feeling”) through this transitive ladder of Greek, Latin and then French. Even “telepathy”, with “tele” meaning “distant” or “at a distance”.
So there you have it; the two words are not exactly interchangeable, although I’m sure all but the most ardent pedants would forgive you for mistaking one for the other from time to time.