Oh, Beth, I am afraid we have to find the points from Buddism.
Chinese culture was much influnced by Buddism and Confucius thoughts. Buddism says: one's destiny is decided and not changable. Your current life destiny is the result of your past lives. You can find the reasons in your past lives for all the happenings in your current life. If you hurt others or made others suffering in the past life, that was a kind of sin or debts( 孽债nie4zhai4), they will come for revenge in your following lives to make you suffer too. If you were kind or helped other in your past lives, which was a kind of credits, they will come and thank you or make you happy in the following lives. In this way, this religion to tell people should be good to others.
That is why Chinese people will yell " 我上辈子造了什么孽了!?" when they were suffering too much. They are asking what sins they made in the past life.
Chinese people also like to say " 别伤心了,你们可能还是缘分没到吧!”to console a sad guy who just lost love. If the girl and boy never had something special happened in the past lives , that is to say their connection is not much enough to make strong feeling happened this life
In a word, nice people will end with a happy end and bad people will end with a sorry end. But why are some really bad guys enjoying instead of suffering? Buddism tells " 不是不报,而是时候未到”( it is not the time for them to suffer, you will get that at the right time in the following period or lives )
After so long explanation, let us come back to your question. 命运 = destiny 命= whatever you deserved 运 = how you go on the way to your destiny 缘分 = connection, which means whether you had met and had somethng special happened with someone in the past lives. This connection can be positive ( 善缘)or negative (孽缘). Generally, in nowadays daily life , Chinese people love to call positive connection 缘分. But in religion, it can be both positive or negative.
Anyway, cultural things are confusing sometimes to a foreigner. I am also learning about christian or cathelic church culture now. Too many questions to ask my friend here. :) Good luck!