The difference between sympathy and empathy is that one is emotional while the other is cognitive. Sympathy is feeling compassion or pity for another person when being made aware of their emotional experience. Sympathy is almost replicating that emotional experience or feeling pain from witnessing another's pain.

Empathy, on the other hand, is utilizing the theory of mind in order to put yourself "in their shoes." Theory of mind is the conceptualization that every person has their own personal experience that is just as valid as ours. It is understanding the ramifications of the experience and is not always accompanied by emotion.

An example would be the witnessing of a friend crying. If someone witnessed a friend crying and started feeling bad because that friend is crying, that would be sympathy. On the other hand, empathy would be understanding WHY that person is crying.
While sympathy is all emotion, empathy is no emotion at all.

Empathy is a term that came after the existence of sympathy. In fact, empathy became a popular term in the 1800s and sympathy came into existence in the 1500s. Empathy is known for the capacity to understand someone else's point of view.
Both can be useful in different situations. For instance, in a business or professional situation, it would be highly useful to utilize empathy in order to understand the perspective of potential business partners or understand what drives other people to behave the way that they do.

On the other hand, sympathy is especially crucial in personal relationships (including friendships) because sympathy is what helps people feel emotionally bonded to one another. People tend to feel much more emotionally close to people who feel sympathy for them during difficult situations. Sharing emotional experiences is what creates intimacy.

Both sympathy and empathy are important tools that people can use to make their lives better, but they should not be confused.

If someone says that they are sympathetic, they may not completely understand the plight of the other person. Instead, they may only understand that the person they care about is in pain, and they feel bad to see that pain. They want the pain to dissipate.

If someone says that they are empathetic, then they may understand exactly what is happening to the other person, but they may not exhibit the supportive gestures that the other person may need in order to have comfort.

People tend to naturally couple sympathy and empathy together because the two enhance each other. More cognitive understanding tends to increase sympathy, and more sympathy tends to increase the desire to fully understand the perspective of the person who is suffering, which would result in empathy.

While sympathy provides comfort, empathy from another person provides the feeling of being understood and accepted. Both are important, but they should not be confused.