Worry is when we have undue anxiety about something that cannot be helped. In such a situation it is best to pray and trust that the Lord will only allow what is best for the person/situation. If we give in to the worry and it takes our focus off of the Lord, then we are only making the situation worse. The evil one likes to see us unsettled, because it takes our focus off of Jesus.
Compassion is when we have empathy towards someone and want to help them in their distress. We do the best we can to be a good listener, and offer our help and understanding if there is something we can do. True compassion is unselfish and seeks the good of the other person.
DISCLAIMER: Catholic Answers has turned over the archive to Catholic-Questions.org and no longer owns, manages, or moderates the forums. For additional apologetics resources please visit www.catholic.com.