All from the same source who is God, so not different in the sense that seems to be what is meant by your question.
Jesus founded ONE Church, One faith, on ONE Lord. He conferred upon Peter the mission of leading that Church and then gave to him the faith necessary to fulfill that mission. God called him, Jesus redeemed him and the Holy Spirit strengthened him. The Trinity, three in one, different yet the same.
So, yes, I believe that the rock is all three of those things, Christ, Peter’s confession and Peter’s faith.
Yes; that's what your chosen church teachs.
Too bad that Scripture does not record that fact.