Chinese 机 and Japanese 机 are not actually cognates at all, because Chinese 机 derives from 機 which in turn derives from 幾, while Japanese 机 derives from 几).Lao Kou wrote: As we've seen, Chinese 机 and Japanese 机 are cognates, or at least have a mother-daughter relationship. As GrandPiano points out, Chinese 机 is used in compounds and not left alone, floating in space, like 机 in Japanese, so it'd be:
A false friend should be cognate but with a different meaning. ZH機 and ZH机 are cognate and have the same meaning, so they can't be false friends.
a false cognate would be something that looks/sounds similar and has a similar meaning, but is not actually cognate. ZH机 and JA机 are not cognates, and they look identical, but they have totally different meanings, so they're really not false cognates either.
So they seem to fall in the realm of "other unfortunate coincidences".