Concise Bible Dictionary:

1. From γεμμάω, “to beget.” This word is used
a) for the natural generation of mankind, as in Matthew 1.
b) for the spiritual generation of the Christian. Paul wrote to the Corinthians, “In Christ Jesus I have begotten you through the gospel” (1 Cor. 4:15); and of Onesimus he says, “whom I have begotten in my bonds” (Philem. 1:10) signifying that he had been the means of their conversion; for the Christian is begotten of God (1 John 5:18; 1 Pet. 1:3).
c) for the Lord Jesus, when He became a man, conceived (begotten) of the Holy Ghost (Matt. 1:20); and declared in those words of Jehovah to Him, “Thou art my Son; this day have I begotten thee” (Psa. 2:7; Acts 13:33; Heb. 1:5; Heb. 5:5).
d) μόνοτγενής, a name of peculiar affection for the Lord Jesus in His eternal Sonship as existing before He came into the world, and referred to as the only begotten Son, the only begotten of the Father (John 1:14, 18; John 3:16,18). It is here used as the equivalent of a Hebrew word (yachid) which signifies “only one,” and hence “darling” (Gen. 22:2; Psa. 22:20; Psa. 35:17).
2. πρωτότοκος, applied to the Lord Jesus as “the first-begotten,” or rather “the firstborn” as marking His supremacy above all. The angels were called to worship Him when He was brought into the world (Heb. 1:6); and He is said to be the firstborn from among the dead (Rev. 1:5).