These two words are often used interchangeably, but there is a meaningful difference. Understanding it will help you use both words with confidence.
A feeling of care and concern for someone who is suffering; you try to understand what they are going through, even though you may not have had the same experience yourself.
Examples
A deep understanding of another person's feelings because you have had the same, or a very similar, experience yourself.
Examples
Both words also appear as verbs — empathize and sympathize — and are used in the same contexts with the same distinction.
empathize
sympathize