Sympathy at least implies superiority of the giver to the receiver. A person without grief expresses sympathy to a person experiencing grief; a smart person expresses sympathy to a dumb person. Examples, for good or ill.
Empathy is more of a sharing among equals. One can empathize with a person experiencing grief because one has experienced grief one’s self or has otherwise achieved an understanding of it. A smart person recognizes gaps and flaws in his own intellect and can relate to a person who, overall, has fewer intellectuals gifts.
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