Thank you kindly. I think that sums up the Chinese “yuan” well. ^-^

You mentioned the chance meeting, which is always the start of the relationship whether between two lovers, teacher and student, or even a child to parents. But the time spent and the evolution of that relationship should to be taken into account, not just the initial encounter. Yuan jin itself implies that yuan has run its course, so the idea of passage of time (regardless of time) in yuan seems important. Strong yuan might make for a longer time together with lives truly intertwining, while light yuan may be your just running into someone on a train with whom you have 20 minute conversation – but the would be considered yuan nonetheless.

Ming yun on the other hand, I suppose, can refer to the end state when yuan jin is reached, though it seems to be used almost exclusively to heighten drama around an incident. In all, the idea of fate, is certainly present in both, though the English concept seems to lack the subtlety present in the Chinese (and Japanese) terms.

For MoG, I vaguely recall something about “on” (恩) – as in Sayuri thinks of him as her “onjin” (恩人), because he had shown her kindness when she was young and helpless… But then again, it is only what I vaguely recall.

I read the manga of Kenshin and watched the movie of MoG ages ago, but cannot recall any definition of enishi. (But then it could just be me growing old and forgetful).

Yes, I think determinism is similar to enishi. You don’t hear the term “determinism” spoken in everyday conversation in English, though enishi is every much a part of everyday conversation in Chinese and Japanese.