Empathy is your ability to understand other people, which gives you the ability to figure out when they are lying, determine whats important to them (by assessing their aspects), provide the right kind of comfort when they are socially or mentally damaged, and let you get a feel for a way the conversation is going (represented by it determining initiative).
Rapport is your ability to get along with people, and how good you are at conversation. High Rapport lets you give good first impressions, respond to social attacks with ease, conceal your motives (by shutting down, not deceiving), and lead the conversation in a way that will tend to get the other person to end up agreeing with you.