Strictly speaking, the Pope is the Bishop of Rome in that he has all ordinary, proper, and immediate power that is required for the exercise of his pastoral function within the territorial limits of the Diocese of Rome.
However, the Bishop of Rome is also the successor of St. Peter, the first Bishop of Rome.
The Power of the Keys which Jesus Christ gave to Peter, indicates that Peter and his successors are the shepherds or leaders of the Church.
Jesus also gave Peter the power to bind and loose, a power which was shared with the other Apostles; this power continues in the Church today in the persons of the Pope and bishops as their successors.
It is to all of the Apostles, together with St. Peter, that the Lord gives the mission to “go forth and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit, teaching them to observe all that I have commanded you.”
Just as the Pope is the visible source and foundation of unity for the universal Church, individual bishops, in union with the Pope, are the visible source and foundation of their own particular dioceses.