Christ used the word petros = a stone for Peter. In the same verse He says, "on this rock..." In this case he uses the word petra = a large rock. Why the change?
Because He was not building His church on Peter, but on the truth spoken by Peter two verses earlier:
"And Simon Peter answered and said, Thou art the Christ, the Son of the living God."
Christ is the rock, the firm foundation, the truth on which He built His church. People are not swayed to come to the Lord by Peter, but by knowing the truth of who Christ is.
Christ did not speak Greek. Check the Aramaic