What are the differences between exalted, resurrected, and translated beings?
A resurrected person is one who has been raised from death to life, never again to die. The best example of this is Jesus who had a body that could be handled (Luke 24:39) and accommodate the consumption of fish and honeycomb (Luke 24:42). Joseph Smith taught that “resurrected personages hav[e] bodies of flesh and bone” (D&C 129:1). This gift of physical life will be given to all who have ever lived or will live. Paul testified that “in Adam all die” as our common mortal inheritance. “Even so,” he adds, “in Christ shall all be made alive” (1 Corinthians 15:22) through our common gift of immortality. These fathers of mortality and immortality are placed together as bookends. This work of the Atonement is central to God’s work and glory, which is “to bring to pass the immortality … of man” (Moses 1:39).
An exalted person is one who has received eternal life. The term itself means to be raised up high (ex altus), and the scriptures are clear that we are not to exalt ourselves (D&C 63:55, D&C 112:15, Matt. 23:12), but rather to exalt God in praise or power (Acts 2:33, Philippians 2:9, Psalms 34:3, 108:5, 118:28) and our fellowman in the spirit of Zion (2 Cor. 11:7, D&C 104:16). In the fullest sense that you mention here, God will exalt the faithful (1 Peter 5:6). Christ plays upon the literal imagery of this term by contrasting man’s judgment when raising up or lifting up Christ for scrutiny and God’s judgment when each of us are lifted up. “[M]y Father sent me that I might be lifted up upon the cross; and after that I had been lifted up upon the cross, that I might draw all men unto me, that as I have been lifted up by men even so should men be lifted up by the Father, to stand before me, to be judged of their works” (3 Nephi 27:14). Revisiting the concept in a new context, the blessed are “lifted up at the last day” (3 Ne. 27:22), or exalted. Exaltation is greater than resurrection and so requires some effort on our part. Those lifted up in exaltation “repent, … come unto [Christ] and [are] baptized in [His] name, … [are] sanctified by the reception of the Holy Ghost” (3 Ne. 27:20). Note that those who are exalted are a subset of everyone who receives the resurrection. Not all who will be resurrected will receive exaltation, but all who are exalted have of necessity been resurrected. This work of the Atonement is central to God’s work and glory, which is “to bring to pass the … eternal life of man” (Moses 1:39).
A translated person is one who has been changed to a state where he or she is no longer subject to the vicissitudes of physical life, such as being subject to death, but who has not yet been resurrected (3 Ne. 28:38-39). This person will at some future point die and be resurrected, just as everyone else must (3 Ne. 28:40). The inhabitants of the entire city of Enoch were translated (D&C 45:11-12). In later times, we know that Moses and Elijah were translated (2 Kings 2:11), and the Book of Mormon gives us reason to believe the prophet Alma was translated (Alma 45:19). Moses and Elijah in particular needed to lay hands on Peter, James, and John to transmit priesthood keys before the resurrection (Matt. 17:1-3) and thus needed to be preserved in the flesh. We are also told that the three Nephite disciples (3 Ne. 28:27-29) and John the Beloved (D&C 7) were translated in order to be able to serve on the earth and help the work of the Lord.