ANSWER: The two New Testament verbs are ἀγαπάω (agapao) and φιλέω phileo, the first the love of choice, the other the love of feeling. Peter in his answers insisted on using the latter, till finally Christ, who had twice used the former, uses the verb which Peter preferred. The whole question turns on Peter's conception of the two verbs with regard to their relative strength. For in one respect Peter's favorite verb is stronger because it is warmer and more emotional, and Jesus has himself used it in John 16:27, "Ye have loved me and believed that I came from the Father." Others think that Peter in his penitence shrank from using the word indicating decided love of the will, instead of the term expressive of inclination and emotion, and that he was grieved and humbled because he could not affirm the strong kind of love that Jesus was seeking. The reader is left to choose between these two theories. I think it was very much like Peter to use what appeared to him to be the stronger verb and to bring Jesus to use his term.
— from Steele's Answers pp. 53, 54.