Well since they joined "one and only" and "unique" it would be a paraphrase of "monogenes" (only begotten or uniquely begotten).
Christians should understand that the Holy Spirit deliberately calls Jesus "the only begotten Son of God" since this is a "begetting" unlike any other -- it is an eternal Father-Son relationship within the Godhead which excludes any mother. Christ was the only begotten Son from all eternity, as well as the eternal Word of God.
Actually, in John 3:16 it is Jesus Himself calling Himself only begotten. It is interesting that John used this particular combination. While mono is obvious...one only, or unique...the ginomai part has been translated over 50 times as
done and over 50 times as come, become, made and fulfilled. Strong‘s describes it as a word that is translated in the KJV as be assembled, be (come), be (brought to pass), arise, continue etc.
John wrote his gospel to specifically refute early heresies, and to prove Jesus is the literal Son of God. Also, that Sonship was in context pre-incarnation...not in reference to Jesus' birth in Bethlehem. So John's use of that particular word is in direct pertinence to his purpose in writing...the real pre-invcarnate Sonship of Jesus. The instances John uses the word are..
―And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten (Gr. monogenes) of the Father,) full of grace and truth. John 1:14
―No man hath seen God at any time, the only begotten (Gr. monogenes) Son, which is in the bosom of the Father, he hath declared him. John 1:18
―For God so loved the world, that he gave his only begotten (Gr. monogenes) Son, that whosoever believeth in him should not perish, but have everlasting life. John 3:16
―He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten (Gr. monogenes) Son of God. John 3:18
―In this was manifested the love of God toward us, because that God sent his only begotten (Gr. monogenes) Son into the world, that we might live through him. 1 John 4:9
This was a parent-child relationship. This was obviously the divinely inspired thought that led John to use this word. The latter is very important to realise. This has nothing to do with the incarnation. We are talking here in terms of Christ‘s pre-existence. It would be reasonable to think that John recorded Jesus as saying of Himself (John 3:16) that He was the only one who is "come to pass" or who has been "brought to pass” of God. I would also suggest that based on that reasoning, and along with Jesus later declaration that He "came forth from the Father" and that the life He has was derived from the Father (the same life He has to share with us...eternal life) is why I struggle with the trinitarian concept of 'eternally begotten'. There can be no literal "brought to pass" if Jesus was around for as long as the Father. I believe at some point in eternity, Jesus was "brought forth" . How that came to be and the process through which that took place we of course aren't informed...but the specific use of 'monogenes' throughout John's writings lends itself to that idea which cannot easily be sustained in relation to eternal past existence. But hey, this is just me ruminating and as I have said several times previously, when it comes to the nature of how the Godhead is comprised together and the members' relation to one another, I treat with caution with no declaration of absolutes or formulas.