It's true that these are not exactly alike. I was keeping it short to address the OP.
I think one is born with compassion. I think you may be able to learn sympathy from one's early upbringing. Empathy is also, I believe, innate.
In my early childhood my parents "talked" about caring about how terrible racism and bigotry is....and talked about "caring" about those less fortunate.
But my mother wrote very few checks to any charity. She didn't extend her sympathy to me or anyone she felt was "undeserving". She had no idea how to bring up a daughter, tho there had been 2 girls and 4 boys in HER original family (and I was an only child.)
When I (very early) had the instinct to "help" people, she wanted to know why I didn't ask HER what I could do for her.....instead. In fact she made me feel that I was lacking in feeling for HER by wanting to help others.
It wasn't until I began to learn astrology and was able to read both my own chart and hers that I felt we might have come from different planets. It was a blessing to know that we were just different and born that way.
I never saw her cry during a movie or show any compassion when a friend's husband died or even when her friends began to be ill and died. She never spoke to me or at home about these tragedies or feeling terrible for her friends.
She put up with our dog when I was a kid, because my father like him.....but resented the money they had to spend from time to time on the dog.
I never saw any sweetness or selflessness for the sake of another - she was not as bad with my children as she was with me, but they ended up feeling "lacking" (they told me later) and it was hard to balance the negativity they got in her care when I had to work part time and they had to stay with her after school. I know she resented this. Her only grandchildren, girls, and only 2 days a week.
This above description is a very small part of this oddity in character as I saw it.
When I began doing readings when I was studying astrology in the early days, she would ask me every week....are you getting paid for this yet? WHEN are you going to get PAID for this? Of course she also had the mind set of the "victim" and frankly, knowing this helped me deal with her in her last years.
She only had one planet in water, Neptune: but....she had several in Capricorn - opposing it.
So - you're born with compassion...it may not fully develop until the 3rd Jupiter return, but it should begin to be felt at 12 or 13.
LIN