I have suggested that while there can be differences between the meaning of agapaō and phileō, those differences are because of the context in which the words are used and are not necessarily inherent in the words themselves. This understanding directly influences the way one understands what is going on between Peter and Jesus in John 21:15-17.
The author of the Fourth Gospel is using agapaō and phileō as synonyms in this interchange between Jesus and Peter, and the point of the narrative is not about the quality of Peter’s love for Jesus, but Jesus restoring Peter. Peter’s threefold affirmation of love for Jesus (Jn. 21:15-17) matches Peter’s triple denial of Jesus (Jn. 18:17, 25, 27). Peter needs to be restored from his denials and return to fishing (Jn. 21:3).
John used four sets of synonyms in relating the restoration scene between Jesus and Peter (as reflected in the above chart). There are synonyms for 1) “love” – agapaō and phileō (by the way, Hebrew and Aramaic do not have different verbs for expressing love, and one of those languages would have been what was spoken); 2) “know” – oida and ginōskō (reference to the same knowledge); 3) “feed” or “care” – boskō and poimainō (reference to the same activity); and 4) “sheep” and “lambs” – arnia and probate (reference to the same group).
Notice also that the text reads that “Peter was grieved because he said to him the third time, Do you love (phileō) me?” (Jn. 21:17). Yet, as the text stands, Jesus did not literally ask Peter about his phileō three times. What Jesus did was ask Peter about his “love” three times, using agapaō and phileō interchangeably in the text to communicate “love.”