Elder Bruce R. McConkie helps us understand how Christ fulfills both roles:
Although Christ—the Firstborn in the spirit and the Only Begotten in the flesh—is the Son of God the Father, and as such is a separate and distinct personage from the Father, yet there are three senses in which Christ is called the Father. These are clearly set forth in a document entitled, “The Father and the Son: A Doctrinal Exposition by the First Presidency and the Twelve.” ([James E. Talmage,] Articles of Faith, 465–473.)
Accordingly, the Father puts his own name on the Son and authorizes him to speak in the first person as though he were the Father. This is similar to the situation in which Christ puts his name on an angel so that the designated heavenly ministrant can speak in the first person as though he were Christ himself. (Rev. 1:1; 19:9–10; 22:8–14.) Thus it is that our Lord can begin a revelation by saying, “Listen to the voice of Jesus Christ,” and shortly thereafter speak of “mine only Begotten” (D&C 29:1, 41–46), such latter expression being made by Christ, but under that divine investiture of authority which permits him to speak as though he were the Father. (D&C 93:3–5; Mosiah 15:1–5.) (Mormon Doctrine, 2d ed. [Salt Lake City: Bookcraft, 1966], 130)