"The Christ, the Son of God"

When Peter confesses, "You are the Christ, the Son of the Living God," he is not making a definitive statement about the deity of Jesus. When Peter calls Jesus "Christ," he is affirming that Jesus, as a descendent of David, is the final fulfillment of the promise of a king to sit on David's throne. When Peter calls him "Son of God," he does not mean by that title what we mean by that title.

So what does Peter mean when he says to Jesus, "You are the Christ, the Son of the Living God"? And why is it fair to say that Peter is saying more than even he himself understands he is saying about the person of Jesus Christ?