I edited a part of https://blog.udemy.com/empathy-vs-sympathy/ for grammar and readability:
The Etymology and Dictionary Definitions of Empathy vs. Sympathy
Part of what complicates differentiating empathy and sympathy is: both words sound very similar and both concepts espouse similar things in practice. Let’s look first at the definitions of the two words and see what can conclude:
Empathy:  the action of understanding, being aware of, being sensitive to, and vicariously experiencing the feelings, thoughts, and experience of another of either the past or present without having the feelings, thoughts, and experience fully communicated in an objectively explicit manner;  also : the capacity for this
Sympathy: (1) the feeling that you care about and are sorry about someone else’s trouble, grief, misfortune, etc. : a sympathetic feeling. (2) an affinity, association, or relationship between persons or things wherein whatever affects one similarly affects the other.
The two are obviously very similar. Certainly, we begin to see a picture emerge. Conventional wisdom holds that where empathy is the feeling of “walking in another’s shoes,” sympathy is more of a feeling of being sorry or bereft, even on behalf of another person. After all, if you were to walk into any card or greeting store, you would likely find a number of “In Sympathy” cards to help express the feeling of loss you may have for another person, even if you are not going through the same situation. Still, the two are very alike, and you may still want further clarification for what the exact difference is between the two. The definition alone may not be quite enough to help separate sympathy from empathy, so let’s look at the etymology of each word.
Etymology is the study of the origin of language. Each word can be broken down into roots, suffix, and prefix, and each of those components have an origin; for instance, words with a Latin, Greek, or Germanic root are very common in the English language. So let’s look at the etymology of empathy vs. sympathy and see if we are able to discern any further information. In this case, we see that each word has its root in ancient Greek.
Empathy: Formed from the ancient Greek word empatheia with the prefix en (English: in) + the root pathos (feeling or passion), the word literally means to be “in feeling”.
Sympathy: Also formed from ancient Greek, the word “sympathy” comes from the old sympatheia and was formed from the prefix sum (with or together) and again with the root pathos (which here can mean either feeling or suffering), and so can here mean either “with suffering”, “together suffering”, or “together feeling”.
This clarifies a little more how each words was developed and meant to be used, right? Once we look more closely, we can see the main difference in the two words: to empathize with someone, is to assume their feelings upon yourself and allow yourself to feel what they feel.
Sympathy, on the other hand, is more the act of commiseration. It is an acknowledgement that you can't possibly feel the same way or truly share another’s grief, but that you can understand it. It’s a little like the difference between, “I know how you feel”, and “I can imagine what that feels like”. For some reason, of late, sympathy has gotten something of a bad rap, but that’s a little unfair. Both sympathy and empathy have their place in the social sphere and both are valid ways of relating to someone.