I had done an exegesis for Dr. Schubert two or three years back on John 21:15-17 and I dug up some of my research from that time in the form of journal articles. Scholarly consensus seems to indicate that the verbs are synonymous in John’s Gospel. I’ll quote from a Semeia article, not because I think it authoritative but because it expresses the matter the best, with examples:

Most ancient Greek commentators and Reformation scholars, as well as most present-day commentators regard these two verbs as synonymous in the Fourth Gospel (Barrett; Brown; Bultmann; Schnackenburg). But British scholars of the last century as well as several present-day commentators and translators argue for a clear distinction between them. Some, in accord with the earlier, classical usage, see in phileo a higher form of love than in agapao. Others argue for the reverse relationship between the two.

I think it is wrong to maintain a distinction between these two verbs in this passage with regard to the kind of love to which they refer. In other clearly parallel passages, the Fourth Evangelist uses them interchangeably. I cite only two examples. In 14:23 and in 16:27 Jesus teaches his disciples that, if a person loves him, the Father will love that person in turn. In the former passage the verb is agapao and in the latter phileo. Likewise the Beloved Disciple is described as such using both verbs: in 20:2 using phileo, and in 13:23; 19:26; 21:7, 20 using agapao.

In addition to this parallel use of agapao and phileo, there is another passage in which nouns deriving from the same root as these two verbs are defined in terms of each other. In 15:13 Jesus teaches that the greatest love ( agape ) which a person can express is to “lay down his life for his friends ( philon ).” We shall see below that the reason Jesus is questioning Peter’s love in 21:15-19 is precisely because Peter had promised to lay down his life for Jesus ( 13:37 ) and had failed to live up to that promise ( 18:15-18, 25-27 ). Therefore, when 15:9-15 is part of the context of our reading or hearing of 21:15-17, the use of both agapao and phileo in the latter passage may prompt us to recall that, in the teaching Jesus gave to his disciples the night before he died, he defined both “love” and “friendship” in terms of being willing to lay down one’s life.

It was necessary to clarify the relationship of agapao and phileo in 21:15-17 in order to describe the literary structure of that conversation. The fact that they are synonymous means that the content of Jesus’ question to Peter does not change at v 17 with regard to the kind of love he has in mind. Rather, the question remains the same throughout the entire sequence, except for the dropping of the comparison after v 15. He asks the same question for the third time; he does not alter the question on the third time (Schnackenburg). Likewise, Peter’s pain after Jesus’ third question results not from an alteration in Jesus’ question from one kind of “love” to another. He is pained because Jesus asks him the same question for the third time, after he had already answered Jesus twice in the affirmative! In other words, there is only one real question in this little conversation between Jesus and Peter, and Jesus is not satisfied with Peter’s answer to that question until the end of v 17, after which he lays it to rest.

So, I think that “love” in our translations conveys the content of these passages. We do not need to suspect otherwise or feel cheated by any perceived shortcomings of the English language. I trust that if there really were a difference between these Greek verbs, translators would have found a way to express that difference in English.