Why is the history and culture of northern Africa different from that of central and southern Africa?
The most important factor in causing this is geography.
Northern Africa is really quite separate from Central and Southern Africa. It is separated from them by the Sahara Desert. Moreover, it is connected to the Mediterranean world. For example, because it was connected to the Mediterranean and to the Middle East, Northern Africa became Muslim soon after the rise of Islam in Saudi Arabia. Islam did not spread nearly so easily into the other parts of Africa because of geographical barriers. For this reason, North Africa is culturally Arab while other parts of Africa typically are not.