Let me show you that Peter did not see any distinction between the words Christ used for 'love'.
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Why does John say Jesus asked Peter a third time 'Do you love [phileo] me?', when in fact phileo is only used once? How does John get to a count of three, when phileo was only used once?
This is a really good point which I hadn't noted before. It's also strengthened by the observation that each time Peter answered he agreed with Jesus.
Q:Do you agape me?
A:Yes Lord, I phileo you
If Peter actually meant "No Lord I can't claim to agape you but I do phileo you" then he wouldn't have replied "yes Lord".
I did used to think there must be some significance in the different words (though never quite sure what), but this discussion and examining the passage itself confirms for me that it is better not to try to read too much into it.
D