How can empathy be distinguished from sympathy?

Solution 1:

Sympathy noun 1 Feelings of pity and sorrow for someone else’s misfortune - ODO

Empathy noun The ability to understand and share the feelings of another. - ODO

With sympathy, you feel sorry that someone else has experienced something bad even if you have no idea how they feel. With empathy, if they are sorrowful, you feel their sorrow.

Etymology is not always accurate when considering current usage, but in this case, it is germane:

1908, modeled on German Einfühlung (from ein "in" + Fühlung "feeling"), which was coined 1858 by German philosopher Rudolf Lotze (1817-1881) as a translation of Greek empatheia "passion, state of emotion," from assimilated form of en "in" (see en- (2)) + pathos "feeling" (see pathos). A term from a theory of art appreciation that maintains appreciation depends on the viewer's ability to project his personality into the viewed object.

Not only do I see gravity and modesty and pride and courtesy and stateliness, but I feel or act them in the mind's muscles. This is, I suppose, a simple case of empathy, if we may coin that term as a rendering of Einfühlung; there is nothing curious or idiosyncratic about it; but it is a fact that must be mentioned. [Edward Bradford Titchener, "Lectures on the Experimental Psychology of the Thought Processes," 1909]

- etymonline.com

Here are a couple of citations that reinforce this view:

In 1909, the psychologist Edward Titchener translated the German Einfühlung (‘feeling into’) into English as ‘empathy’. Empathy can be defined as a person’s ability to recognize and share the emotions of another person, fictional character, or sentient being. It involves, first, seeing someone else’s situation from his perspective, and, second, sharing his emotions, including, if any, his distress. - Neel Burton, "Empathy Vs Sympathy", Psychology Today
Empathy is the ability to experience the feelings of another person. It goes beyond sympathy, which is caring and understanding for the suffering of others. Both words are used similarly and often interchangeably (incorrectly so) but differ subtly in their emotional meaning. - "Empathy vs Sympathy." Diffen.com. Diffen LLC, n.d. Web. 14 Aug 2016. < http://www.diffen.com/difference/Empathy_vs_Sympathy >

The page from diffen.com cited above has the following examples:

Empathy: "I know it's not easy to lose weight because I have faced the same problems myself."
Sympathy: "Trying to lose weight can often feel like an uphill battle."

Solution 2:

There's definitely some disagreement about the distinction between sympathy and empathy, and which of the two connotes a closer emotional connection, at least between Merriam-Webster and other dictionaries. I think this confusion is because sympathy has multiple definitions:

feeling the same emotions as someone else, especially if you are or have been similarly personally affected
feeling pity
understanding or agreement

whereas empathy only has one definition:

feeling the same emotions as someone else

Essentially, empathy is one of the definitions of sympathy. However, it seems that this first definition here of sympathy is in decline, because sympathy can also be interpreted meaning mere pity, and if you wanted to unambiguously say "feeling the same emotions as someone else", you'd probably just say empathy.

Merriam-Webster draws the same distinction that you draw:

Sympathy, constructed from the Greek "sym," meaning together, and "pathos," referring to feelings or emotion, is used to describe when one person shares the same feelings of another, such as when someone close is experiencing grief or loss. Empathy is a newer word also related to "pathos," but there is a greater implication of emotional distance. With "empathy" you can imagine or understand to how someone might feel, without necessarily having those feelings yourself.

Dictionary.com, however, says, however, says

Nowadays, sympathy is largely used to convey commiseration, pity, or feelings of sorrow for someone else who is experiencing misfortune. This sense is often seen in the category of greeting cards labeled “sympathy” that specialize in messages of support and sorrow for others in a time of need. You feel bad for them … but you don’t know what it is like to be in their shoes.

empathy […] is now most often used to refer to the capacity or ability to imagine oneself in the situation of another, experiencing the emotions, ideas, or opinions of that person.

sympathy is feeling compassion, sorrow, or pity for the hardships that another person encounters. […] empathy is putting yourself in the shoes of another, which is why actors often talk about it.

Similarly, Lexico says:

Empathy means ‘the ability to understand and share the feelings of another’ (as in both authors have the skill to make you feel empathy with their heroines), whereas sympathy means ‘feelings of pity and sorrow for someone else's misfortune’ (as in they had great sympathy for the flood victims)

Lexico provides the following definitions (abridged):

sympathy:

feelings of pity and sorrow for someone else's misfortune.

understanding between people; common feeling.

[example sentence] ‘He listens politely and patiently to Dabii's request, with a smile of sympathy and understanding.’

The second definition here sounds a lot like empathy.

For sympathy, Merriam-Webster adds the definition

the act or capacity of entering into or sharing the feelings or interests of another / the feeling or mental state brought about by such sensitivity

Lexico defines empathy simply as

The ability to understand and share the feelings of another.

Merriam-Webster defines it as:

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

Solution 3:

Empathy — ODO

noun the ability to understand and share the feelings of another.

In other words, it’s not about sharing similar experiences with somebody else: it’s about sharing feelings with somebody else. You can empathize with somebody even if you have never found yourself in similar circumstances. What matters is whether you can understand their feelings and put yourself in their shoes.

One of Oxford Dictionary’s examples of correct usage illustrates this:

“There is a frightening lack of empathy and of understanding of the condition of the elderly.”

The sentence isn’t saying that people have not experienced the condition of being elderly! The point is that people who haven’t reached old age have failed to properly feel for the elderly.

Sympathy, as you said, is about feeling pity and sadness because of somebody else’s condition.

Solution 4:

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: [1] 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; [2] 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.