Mormons themselves seem to be confused about their exact description. Most common is the explanation that “an angel is a resurrected or translated body, with its spirit ministering to embodied spirits” (D&C Student Manual, p. 320). An example would be the angel Moroni who supposedly appeared to Joseph Smith. According to the Book of Mormon, Moroni was originally a Nephite leader who was resurrected sometime after his death.
Biblical Christianity teaches that God created angels distinct from humans. They especially serve believers (Hebrews 1:20).