The Greek text of John 21:15-17 indicates that Jesus used ἀγαπᾶν (agapan) for the Greek verb “love,” while Peter used φιλεῖν (philein) in his reply. The explanation often given is that the first word refers to a higher, truer love, whereas the second word means only “to be fond of.”
Unlike Greek, Hebrew does not have two words for “love” that would differentiate between the love of Jesus for Peter and Peter’s love for Jesus. Assuming that Jesus and Peter spoke Hebrew to each other, this Greek distinction is one of myriad indications that the Gospel of John was originally composed in Greek.
-  To be precise, only in the first and second “Do you love me?” addressed to Peter did Jesus use the verb agapan. In his third address, Jesus used the verb philein, the same verb Peter used in each of his responses. ↩