They've got different roots. The bo's origins are Okinawan (ryukyu kobujutsu), the jo styles are Japanese and originated with Muso Gonnosuke. In other words, one is Japanese and one is not.
I believe there have been jojutsu
arts preceding Muso Gonnosuke's. Perhaps the use of the same kind of wooden stick we use for jo practice today started or was popularized with his art, but combative use of a "staff" (not limited to a wooden stick) or jojutsu didn't necessarily start with him.