The answer
In the Holy Gospel of St. Luke 3: 23-38 we read of the Genealogy of the Lord Jesus Christ: the Son of David, the Son of God.The genealogy according to St Luke moves in the opposite direction from that written by St. Matthew, extending farther back beyond Abraham to Adam. Adam as you know was originally the Son of God. Luke's purpose in writing in this manner was to emphasize the Lord Jesus Christ's unity with the entire human race. Thus making the divine sonship available to all through the Lord.
Both Holy Gospel writers (St. Matthew and St. Luke) emphasize the Lord Jesus Christ's Davidic descent through St. Joseph, and His virginal conception and birth. St. Joseph was the "legal" father of the Lord Jesus. So the genealogy that is recorded is through St. Joseph and not St. Mary.
St. Luke's genealogy, as you mentioned, differs from St. Matthew's in that it is thought that St. Matthew derives the Davidic ancestry through King Solomon, a son of David, while St. Luke denotes the Lord Jesus Christ’s ancestry through another son of David, Nathan.
St. Luke describes St. Joseph as the son of Heli. St. Matthew states that Jacob begot St. Joseph. The Old Testament (Deuteronomy 25: 5-6) encourages the brother of a man who died childless to marry the wife of the deceased and raise an heir for his brother. This explains that most probably, Jacob and Heli were born of the same mother, but of different fathers. In other words, when Heli died after a childless marriage, his brother Jacob married the widow, who became the mother of St. Joseph.
Answered by His Eminence Metropolitan Youssef (opens in a new tab)