[Facts] Re: I don't know if this is the correct place to put this question...
Both result from the medieval diminutive suffix -kin.
Jan (a form of John) -> Jankin -> Jackin -> Jack
Hann (a form of John) -> Hankin -> Hank
(Hann/Hankin/Hank could occasionally be used as diminutives of Henry, but they were typically from John)