What was the relationship between Peter and Saint John Paul II?
In 1978, John Paul II began “the mission of Peter” as Bishop of Rome. The Church calls the pope the successor of Saint Peter. John Paul II, homily of October 22, 1978, no. 3; Catechism 882
What the Bible says
Matthew 16:16
Simon Peter answered and said: Thou art Christ, the Son of the living God.
Matthew 16:18
And I say to thee: That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it.
Douay-Rheims Bible (Challoner revision), public domain.
What the Church teaches
The pope, Bishop of Rome and successor of Saint Peter, is the visible source of the unity of the Church.
Catechism 882 · Catechism of the Catholic Church
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Meet Peter and Saint John Paul II.