"The Greek word for 'love' in Jesus' first two questions is different from the word for 'love' in His third question, which is the same word Peter uses in all three answers. It is uncertain whether a distinction in meaning is intended since John often made slight word variations, apparently for stylistic reasons. Also, no distinction is made between these two words elsewhere in this Gospel. In this passage, however, they occur together, and the variations seem too deliberate to be explained on stylistic grounds.The 'love' in Jesus' first two questions (agapao) refers to a love in which the entire personality, including the will is involved. The 'love' in Jesus' third question and in Peters answers (phileo) refers to spontaneous natural affection or fondness in which the emotion plays a more prominent role than will. Whatever interpetation is adopted, the important thing is that in so serious a matter as the reinstatement of Peter, the great question was whether he loved Jesus."
It appears to me that Peter believed the word phileo was a stronger word for love than the word agapeo. He was grieved when Jesus asked him the third time whether he phileo Jesus because he had already answered him twice before that he phileo Jesus. Perhaps what Jesus was trying to teach Peter was the first great commandment: You shall love the Lord your God with all your heart, mind, strength and soul.