When Jesus gave Peter his name (rock) what is the significance that he then said upon a ‘different’ kind of rock he would build his church? When Peter made his famous confession, Jesus responded by saying:


  And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it. (NIV Mathew 16:18)


Looking up the original Greek I see that Jesus is referring to two types of rocks and one is related to the other, but they are not the same.

Peter = Πέτρος, Pétros (a masculine noun) – properly, a stone (pebble), such as a small rock found along a pathway.

Rock = pétra (a feminine noun) – "a mass of connected rock”

The question is, ‘What is the point of bringing in two types of rocks in response to Peter’s confession?’
Ok, so the reality is that there is the appearance of a Discrepancy of sorts in the bible, Peter being called "Pétros", and The church being built on "pétra." 

As a Catholic heres how we interpret this scripture. 


  the Aramaic word kēpā'  meaning rock and transliterated into Greek as Kēphas is the name by which peter is called in the Pauline letters (1 Cor 1:12; 3:22; 9:5; 15:4; Gal 1:18; 2:9, 11, 14) except in Gal 2:7-8 ('Peter'). It is translated as Petros ("Peter") in Jn 1:42. The presumed original Aramaic of jesus' statement would have been in English, "You are the Rock (kēpā') and upon this rock (kēpā') I will build my church." The Greek text probably means the same, for the difference in gender between the masculine noun petros, the disciples new name, and the feminine noun petra (rock)  may be dew to the unsuitability of using a feminine noun as the proper name of a male.Although the two words were generally used with the same meaning, "rock" ... 


Thats found in the note on Mt 6:18 (NAB) in my bible

So another words Jesus used the same word to refer to peter and 'the rock,' which is why Catholics believe that Jesus "built the church" on Peter, and the other popes. Of course, Faith is a gift given by God, and if it wasn't for that faith, Peter, and the rest of the Papacy, and their flock could have never started the church that we know today. So it does make sense, in a way, to say that Peter is a 'little rock' and upon the 'Big rock', the faith Of the head of the body of Christ, (which is given to peter) Jesus builds his church.