1) Matthew 1:1-17, andThe Matthew 1:1-17 and Luke 3:23-38 accounts differ because, Luke follows Mary's lineage (Jesus' blood mother), through David's son Nathan (Luke's genealogy focused on Jesus' descent from God through the virgin birth. It placed no emphasis on Jesus being the descendant of king David) and the Matthew genealogy follows Joseph's line (Joseph being the legal father of Jesus, see below) through David's son Solomon.
2) Luke 3:23-38 (in addition to several other new testament references: Mark 10:47, luke 1:32, Acts 2:29-30, Rev. 5:5, 22:16).
God's promise to David was fulfilled because mary was the biological parent of Jesus.
The virgin birth also addressed the curse God had pronounced upon Jehoiakim. Kingship was an inherited right. By Joseph, Jesus inherited a legal claim to the throne of David. However, he was exempt from the curse of Jehoiakim (Jeremiah 36:1-32, i.e. Joseph's offspring could not claim David's throne because of the curse) because Joseph was not the genetic father of Jesus.