I can't speak for Georgia law but, as far as I know, every jurisdiction provides credit for time served, whether in "jail" or "prison." The only common exception is where the person has two or more sentences to serve from the same or different cases and the sentences are not being served concurrently (but rather are being served consecutively), in which case the person will be receiving credit for one sentence but not the other.
In the State of Georiga, any time that an individual serves in custody after being sentenced will count towards their sentence - whether it is in the local county or city jail or the state prison system. It counts.....good luck!!