If the cases are unrelated, that is a term that must be negotiated by your counsel. It usually does not happen automatically. If you have two different attorneys, you have to make them both aware.
It is something that your attorney would have to request and it would have to be approved by the judge who sentences you last. If you plead guilty to charges in two separate counties, the first judge who sentences you could agree to run the sentences concurrently, but the judge who sentences who second might not agree, so it is important from your attorney to get approval from the second judge.
An exception is if you plead guilty to a felony in one county with a promise of jail/prison time and a misdemeanor in a second county with the promise of jail. The misdemeanor sentence "merges" into the felony sentence and by law will run concurrently.
Are you being sentenced to prison time in both? If so, the first one must be completed before you begin receiving credit on the second one UNLESS there is a plea bargain agreement in the 2nd county that allows that sentence to run concurrently with the first. (If you had been sentenced in one county, there is a presumption that the sentences run concurrently unless otherwise stated.)
If one is a felony and one is a misdemeanor, then generally the felony county would take possession of you and the misdemeanor would simply run concurrently.
If both of the cases are misdemeanors, then you will serve one county until finished, then go to the other county to serve that sentence. However, you will get credit on the one you are in jail on as well as the other one IF the one from the county you are not in jail on currently places a hold or detainer on you while you are serving the first county's time. (Very confusing - sorry.)