The genealogies recorded in Matthew 1 and Luke 3:23-38 are the same until they reach King David’s son. Matthew records King David’s son, Solomon (Matthew 1:6), Joseph’s lineage. Luke is actually recording Mary’s lineage through King David’s son, Nathan (Luke 3:31). Jesus is the seed of the woman.

And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel. – Gen 3:15 KJV

Joseph the Husband of Mary

And Jesse begat David the king; and David the king begat Solomon of her [that had been the wife] of Urias; – Mat 1:6 KJV

…
And Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called Christ. – Mat 1:16 KJV

…
Now the birth of Jesus Christ was on this wise: When as his mother Mary was espoused to Joseph, before they came together, she was found with child of the Holy Ghost. – Mat 1:18 KJV

The Seed of the Woman

Notice in the verses below, each time “the son” is in brackets, these words were added. The original text read, “Joseph, which was of Heli, which was of Melea…” not “the son of.” See at Blue Letter Bible.

And Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was [the son] of Heli, – Luk 3:23 KJV

…
Which was [the son] of Melea, which was [the son] of Menan, which was [the son] of Mattatha, which was [the son] of Nathan, which was [the son] of David, – Luk 3:31 KJV

…
Which was [the son] of Enos, which was [the son] of Seth, which was [the son] of Adam, which was [the son] of God. – Luk 3:38 KJV

God Called Their Name Adam

God called their name Adam at creation! He separated Eve from Adam. But He still referred to them as one flesh with one name, Adam.

This [is] the book of the generations of Adam. In the day that God created man, in the likeness of God made he him; – Gen 5:1 KJV
Male and female created he them; and blessed them, and called their name Adam, in the day when they were created. – Gen 5:2 KJV

Adam Called His Wife Eve

There are only two verses in the garden after the fall where the Bible makes a distinction/separation of Adam and his wife.

And Adam called his wife’s name Eve; because she was the mother of all living. – Gen 3:20 KJV
Unto Adam also and to his wife did the LORD God make coats of skins, and clothed them. – Gen 3:21 KJV

Once the blood was shed and the coats of skin were made, the husband and wife are referred to as one again! I believe this represents God’s reunion with His bride. This is a type and shadow of Jesus’ finished work.

And, having made peace through the blood of his cross, by him to reconcile all things unto himself; by him, [I say], whether [they be] things in earth, or things in heaven. – Col 1:20 KJV

God immediately came looking for them.

The man knew good and evil, and their bodies began to be corruptible (1 Corinthians 15:53-58, 1 Peter 1:23-25).

And the LORD God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever: – Gen 3:22 KJV
Therefore the LORD God sent him forth from the garden of Eden, to till the ground from whence he was taken. – Gen 3:23 KJV
So he drove out the man; and he placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life. – Gen 3:24 KJV

God has never left mankind. Even after Cain killed Abel, God came to Cain and spoke with him. God was still talking to them and instructing them with His Words warning Cain not to let sin rule over him (Genesis 4:7).

And you, that were sometime alienated and enemies in [your] mind by wicked works, yet now hath he reconciled – Col 1:21 KJV
In the body of his flesh through death, to present you holy and unblameable and unreproveable in his sight: – Col 1:22 KJV

Further Study:

The genealogy in Matthew is from Abraham to Jesus, while the book of Luke traces Jesus’ ancestry from Jesus all the way back to Adam. The genealogies are the same from Abraham to David, but from David to Jesus, they are totally different. Both these genealogies were accepted by the early church despite their differences, which is proof enough of their accuracy. It appears that Matthew traced David’s line through Solomon (Matthew 1:6), while Luke traced the royal lineage through Nathan (Luke 3:31), another son of David (2 Samuel 5:14). This would bypass the curse on Jechonias’ seed (Jeremiah 22:24-30). The justification for two genealogies is that Matthew recorded Joseph’s line, while Luke recorded Mary’s line. Luke did say Joseph was the son of Heli, making it appear that Luke was also tracing Joseph’s lineage, but that would not have to be the case. There is scriptural precedent for a man’s son-in-law to be reckoned to the daughter’s genealogy if her father had no sons (Numbers 27:1-11 and 36:1-12 with Ruth 4:6). This could explain the substitution of Joseph’s name for Mary’s in Luke’s account. This is especially appropriate, since Jesus was the seed of the woman (Genesis 3:15) and not the seed of man.

Andrew’s Life For Today Study Bible Notes-Luke 3:23