I keep seeing this around on Tumblr, as part of one of those lists of “untranslatable” words. The way “fate” vs “destiny” is used in this definition seems to me rather muddled — I’m not sure they correspond to the Chinese concepts — though it did make me actually think about said concepts, which I’d never done before.
(I’ve little formal education in Chinese, so this is based entirely on my sense of things as a native speaker. Corrections are welcome.)
Yuan and fen are separate concepts of fate, or what modern English speakers would casually call “karma,” as it applies to relationships between people. (You cannot have either in isolation, only “with” someone else.) Yuan describes the fated intensity of the interpersonal connection. It comes up most often with regard to romantic relationships — the fabled “red thread of destiny” linking lovers — but in actuality, any two people who have a connection they weren’t born into have yuan. Friends choose each other like magnets do. Everyone knows the feeling of immediately and mysteriously “clicking” with someone you just met: that’s yuan. Two people can also lack yuan: that’s the person in your social circle that you can’t make friends with. You may not dislike them, necessarily, you just can’t seem to get to know them — not in a way that matters. They drift through your life, and you drift through theirs.
I’m pretty sure you can also have yuan with things, or places, or larger people-concepts than individuals. The city where things just happen to you, like a leitmotif running through the musical of your life; the band you always meant to check out but never got to see live, because something always came up.
Fen is, literally, “portion.” It’s the amount of relationship you’re accorded by fate: of the time you’re allotted and that you spend on this Earth, what percentage actually involves this person? As far as I know, which isn’t much, only Chinese makes this entirely sensible distinction.
The cliche is that you can have yuan without fen. (To say that you have no yuan AND no fen with someone is somewhat akin to the English expression “don’t know _____ from Adam.”) Compared to “star-crossed lovers,” which implies two people who actively try to get together but are foiled by bad luck and misunderstanding at every turn, this is a much better description of the Brokeback Mountain type of tragic couple. Even of Romeo and Juliet, perhaps. The connection is once in a lifetime, but it’s not in the cards for you to spend that lifetime with each other. Conversely, I’m not sure you can have fen without yuan: or rather, why would you even bother tracking it?