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Agapaō and phileō are two Greek words that are translated by the English word love. They are both found in the context of John 21:15-17.  The text reads, “So when they had dined, Jesus saith to Simon Peter, Simon, son of Jonas, lovest (agapas) thou me more than these? He saith unto him, Yea, Lord; thou knowest that I love (philō) thee. He saith unto him, Feed my lambs. He saith to him again the second time, Simon, son of Jonas, lovest (agapas)thou me? He saith unto him, Yea, Lord; thou knowest that I love (philō)thee. He saith unto him, Feed my sheep. He saith unto him the third time, Simon, son of Jonas, lovest (phileis) thou me? Peter was grieved because he said unto him the third time, Lovest (phileis) thou me? And he said unto him, Lord thou knowest all things: thou knowest that I love (philō) thee.  Jesus saith unto him, Feed my sheep.”  Lidija Novakovic (John 11-21, A Handbook on the Greek Text, p. 326) quotes Porter with regard to these passages, “These two verbs phileō and agapaō, are not true or complete synonyms.  One of the differing components in the meanings of these words appears to be related to levels of esteem (a vertical scale) for agapaō and interpersonal associations (a horizontal scale) for phileō. The definition of a true synonym is that the two lexemes are interchangeable in all contexts (emphasis mine DS).  That simply is not true for these Greek lexemes: there is a major identifiable pattern of usage that is different.”  Porter suggests that even in John 21:15-17, phileō and agapaō are not complete synonyms because of the logic of the dialogue, in which “Jesus has reduced his first question to a simpler question, and he has received a similarly unsatisfactory answer,” which causes him to replace agapaō with phileō in his third question.
What, if any, is the distinction between agapē and philia (the nouns)?  The Greeks had four words for love: eros, storgē, philia, and agapē.  Eros is the Greek word for sexual love.  Storgē defines family and kinship love.  Philia is friendship love.  John the Baptist was the friend of the bridegroom  (John 3:29).  Jesus used the word philos in saying “our friend Lazarus has fallen asleep (John 11:11).  Agapē carries an unfailing regard for, and deeply cherishes, the object of its devotion. It is love and commitment (Hugo McCord, These Things Speak, 128).  When one is 100% committed to something or some person, the word describing such an attachment is agape.  Agape is good will and selfless giving even of one’s own life to help others.  It involves a commitment without thought of gain or loss to the giver, or merit on the part of the receiver.  Ungodly sinners and enemies of God are the recipients of agapē. The Scriptures never use eros, storgē, or philia to define God, but agapē (Rom. 5:6-10; I John 4:8,16).  McCord states, “The towering superiority of agape above the three related words does not mean that it cannot be used to convey the lesser meanings of the related words.  Both phileō and agapaō were in Jesus’ attitude toward Lazarus whom Jesus loved (John 11:5, 11).  The same is true in regard to the disciple whom Jesus loved (John 13:23; 19:26; 21:7, 20).  To His faithful children God extends agape but also philia (John 14:23; 16:27).  Among humans there is no greater devotion than that of laying down one’s life for his friends (agape and philia, John 15:13).  McCord affirms, “Though agape overlaps meanings found in storge and in philia, and possibly in eros, in the New Testament agape at times is in a realm by itself, a sui genesis, a monogenes.  At times, as the sun outshines the stars, agape is more brilliant than all other words.  In certain contexts it is unique, alone, solitary, a super-word, the greatest New Testament sign of an idea (cf. I Cor. 13:13).  Agape is “above all these”: “a heart of compassion, kindness, lowliness meekness, long-suffering” (Col. 3:12-14). “Above all things” God’s people are commanded to practice “fervent agape” among themselves (I Pet. 4:8).  Six noble attributes (faith, virtue, knowledge, self-control, patience, godliness, brotherly kindness (philia) by themselves are incomplete.  They need to be supplemented, “adding on your part” agape (II Pet. 1:5-7) (Ibid. p. 130).  McCord adds yet another thought, “When one understands the exalted position of agape he understands why Jesus did not use phileo in the command to love one’s enemies (Matt. 5:44).  Enmity is the opposite of phileo (friendship), but agape includes both friends and enemies.  It knows no limits (“never faileth,” I Cor. 13:8) in good will and irrepressible devotion (Ibid.).
Sometimes agape and philia overlap, but they are still intrinsically different.  Thayer mentions that “even in some cases where they might appear to be used interchangeably, the differences can still be traced” (McCord, p. 131).
McCord comments on Jesus and Peter.  “If ever there were a person understanding clearly the commitment inhering in agape, and of its superiority over the affection of philia, it was the apostle Peter.  He had bragged of his devotion to Jesus, claiming a deeper loyalty than that possessed by the other apostles:  “If all shall be offended in thee, I will never be offended” (Matthew 26:33).  However, after he had forsaken his Lord, even cursing and swearing, “I know not the man,” upon hearing the rooster crow, his heart was broken.  Bitter weeping displayed his deep shame.  Like Judas, he was a traitor, and he knew it.  All bragging was gone and his spirt was crushed.  After the Lord’s resurrection, when Peter was with the other disciples by the lakeside, Jesus asked him, “Do you love [agapao] me more than these?” (John 21:15). Peter, hearing agape in Jesus’ question, knowing the magnitude of commitment involved in that word, knowing he had betrayed the Savior, could not honestly put the word agape on his lips.  His reply was an evasion, using phileo. In this context the English word “love” does not rightly translate what Peter said: “Yes, Lord, you know that I like you”” (Ibid. 132).  All pride was absent.  Peter embraced humility in his response to Jesus’ question.  Yet, he affirmed his affection for the Lord three times and so healed a significant breach and created a new memory in his relationship with Jesus.
McCord provides a chart showing some contrasts between agape and phileo.

Phileo                                                                         Agapao
Kiss (Acts 20:37; Rom. 16:16                 “not kiss; there is so far no evidence
S of S 1:2)                                                 for that meaning of “a” (Gingrich-Danker)
Friend (Luke 11:5; Jam. 2:25)                 A beloved one (Matt. 3:17; III John 2)
Natural                                                      Learned
Emotional                                                  Volitional
External                                                      Internal
Discriminatory                                           Non-discriminatory
Conditional                                                 Unconditional
Pleasure                                                      Preciousness
Delight                                                         Esteem
Liking                                                           Prizing
Because of                                                  In spite of
Fails                                                              “Never faileth” (I Cor. 13:8)

The chart clearly shows a difference between the two words and so they are not complete synonyms.