In the three repetitions of the questioning of Peter by Jesus on the beach post resurrection, there are interesting variations in the vocabulary. there are two words for love (agapao and phileo), two for tending the flock (bosko and poimaino), to for the flock (arnia and probatia) and two for know (oida and ginosko). A lot of attention has been given to Jesus switching from the so called “higher” word for love (agapao) to the lesser word suggesting friendship (phileo).
F. F. Bruce states that the two words for love are used interchangeably when the OT word is translated, that agapeo does not necessarily indicate a higher sort of love, and John tends to use them interchangeably (the father loves the son in John 3:35 and 5:20 are agapeo and phileo respectively; “the disciple whom Jesus loved” is written with both words 13:23; 20:2). (F. F. Bruce, The Gospel of John, Eerdmans, 1983, p. 441)
We agree that the variation is more stylistic – it is common in Greek and English to vary the words for the avoidance of repetition. The point then seems to be that the three repetitions answer the three denials by Peter in the chapter 18.
With word-studies it is important to look at all the factors before leaping to a conclusion.