empathy is how you show your understandings to someone and share the same feelings
for example;
jon:my dog has passed away and he has been my best friend since i was 1 years old.
emily: i have gone through the same thing with my dog when he passed away . i have also had him since i was 1.
sympathy is just showing sorrow and acknowledging what has happened to them.
jon:my dog has passed away and he has been my best friend since i was 1 years old.
emily: im sorry for your loss. its okay things will get better.
empathy is more efficent and more understanding than sympathy but if you cant understand how it feels to be as a mental illness its okay to sit and listen to the person and try to understand them.
i hope the examples helped.