The verb “αγαπάω” ( pronunciation: agapáo, definition: to love unconditionally) according to Robert Beekes is a compound word from the adverb “άγαν” (pronounced: ágan, definition: too much [1]) and the Indo-European root word pa- which has the meaning “to protect”. [2]
The verb φιλέω ( pronunciation: phileo) in ancient Greece had the same meaning as to “agapo”, until gradually got the meaning of “to kiss”. The word “phileo” is linked to the word “philos” ( written in Greek φίλος , definition: friend) to show the brotherly type of love towards our friends. [2]
Keeping in mind the difference of “agapáo” ( unconditional love) and “phileo” (brotherly love to a friend), let’s explore how the verb “love” is used in John 21:15-17 in the Greek New Testament.
In John 21:15 and 21:16 Jesus asks Peter twice “do you love Me?” by using the verb “agapao”. Peter replies both times “You know that I love You ” by using the verb “phileo. “
In 21:17 for the third time Jesus asks Peter “do you love Me ” by using the verb ” phileo” and Peter replies “You know that I love You” by using the verb “phileo”.
[1]https://en.m.wiktionary.org/wiki/%CE%AC%CE%B3%CE%B1%CE%BD