From Gordon Keddie in his commentary:
"The three questions are, as the saying goes, ‘the same but different’. Much has been made of the two Greek words for ‘love’ employed in this passage—ἀγαπάω / agapao and Φιλέω / phileo. Jesus uses ἀγαπάω twice, and Φιλέω the third time. Peter’s answers all use Φιλέω. The conversation would have been in Aramaic, and we can only assume that the Greek accurately reflects the substance of the original exchange. What this difference amounts to is not very clear. The standard view in recent times has been that the former refers to a higher form of love (a Christian love), while the latter is a lower form (a personal affection, even passion). If that is the case, then Jesus’ switch from ἀγαπάω to Φιλέω with his third question has to be explained as a gracious condescension to Peter’s weak response, and while that sounds wonderful, it really only masks Peter’s failure to express a deeper love for Christ and begs the question as to the true state of his commitment. The older commentators are often either silent, treating them in practice as interchangeable (e.g., Calvin and Puritans like Owen and Manton), or, like the later Puritan Matthew Henry, take the view that Φιλέω was the more emphatic form of love. This last view is now regarded as philologically untenable, but it had the virtue of preserving the obvious thrust of the passage, which is to demonstrate with some force that Peter’s love for Christ was faithful and full.
Most recently, commentators have been warning against overinterpretation of these verbs and have pointed out that they are sometimes used interchangeably (3:35; 5:20; 11:5, 36) and that ἀγαπάω is used in one instance of a distinctly unchristian ‘love’ (2 Tim. 4:10). If we do grant that ἀγαπάω and Φιλέω are practically interchangeable, while still referring to different objects in other contexts, we can acknowledge that Jesus’ conforming to Peter’s language signifies something of both the rising intensity of Peter’s expression of devotion and Christ’s acceptance of this as the ground of his public reinstatement. It is the unfolding of the context that demands this, whatever the precise weight of the words themselves may or may not be.
The differences between Jesus’ three questions, then, are not so much attributable to the verbs employed, but the mounting insistence evident in the delivery of the questions. The first question, ‘Simon, son of Jonah, do you love me more than these?’ inevitably reminded Peter of the foolish boast that implied that he was the most devoted disciple of all (Matt. 26:33). Here was what Manton calls ‘the core of his [Peter’s] distemper’. Jesus is asking, ‘Is thy love surpassing the love of all my disciples?’ Jesus was not interested in Peter or the others rating their love for him on a scale of 1 to 10. His intention was to bring Peter to a humbled testimony of his love so that he should never again fall into the snare of comparing himself to others in a self-aggrandizing way. The second and third questions, by the fact that they were repetitious, searched ever more deeply into his soul and forced him to face more fully the implications of his three denials, and so to come to express more certainly his love for Christ. ‘It is some conviction to a liar to make him repeat his tale,’ observes Manton. ‘A deceitful heart will be apt to reply, that he is not worthy to live that doth not love Christ; but urge it again and again, Do I indeed love Christ? Yea, leave not till you can appeal to God himself for the sincerity of your love: Lord thou knowest all things, and thou knowest that I love thee.’"