Both are forms of commiseration 怜悯:

Empathy 感同身受 — Empathy is the capacity to understand or feel what another being (a human or non-human animal) is experiencing from within the other being's frame of reference, i.e., the capacity to place oneself in another's position

Sympathy 同情 — is the perception 感知 , understanding, and reaction to the distress or need of another human being.