There are three types of empathy: cognitive, emotional and compassionate empathy; each respectively the desire to understand, to feel and to help and support.
EQ guru Daniel Goleman, in reference to psychologist Paul Ekman, elegantly describes the three types of empathy here: https://greatergood.berkeley.edu/article/item/hot_to_help.
Cognitive empathy alone can result in “too cold to care”: “When people try to understand another person’s point of view without internalizing his or her emotions, they can be so detached that they’re not motivated to do anything to actually help that person.”
“And so cognitive empathy alone is not enough. We also need what Ekman calls “emotional empathy”—when you physically feel what other people feel, as though their emotions were contagious.”
“But wait: Emotional empathy has a downside, too”… “In a state of emotional empathy, people sometimes lack the ability to manage their own distressing emotions, which can lead to paralysis and psychological exhaustion.” Some degree of what Ekman calls “cultivated detachment” is called on for.
With compassionate empathy “we not only understand a person’s predicament and feel with them, but are spontaneously moved to help, if needed.”
P.S. Why three chairs? I do this as a coaching exercise: imagine sitting in the first chair and think of what you want to understand about that other person. Then next stand up and move into the second chair. This time, try to feel what the other person is feeling. From thinking with your left-brain, now feel with your heart. Then finally move into the third chair. Now what would you like to do for her/him? I find the chair metaphor a very nice way to transcend empathy from left-brain to heart and finally to right-brain.