I don't know about Michigan, Bingley, but in NY jail is local (i.e., Riker's Island in NYC) and is used for terms under one year.
If you are sentenced to a term over one year, you go to a state prison. (Sing Sing is the well known one, but it a very high security one.. the more common prison is somewhere else.. way, way up state.) i am lucky, and don't have any familiarity with prisons.. and only know about jail from civic's class.

time servered in jail (awaiting/during the trial) can be applied to your prison term.