JOEL - Besides my granddaughter, there are other different types of beings that can be called "angels", which perform a variety of functions to help carry out the work of God on this earth and in heaven.
Whether they have a physical body or not they are all in the form of a human being and, according to Joseph Smith, do not have wings (Joseph Smith, History of The Church of Jesus Christ of Latter-day Saints, 7 vols. 3:392). There are a few scriptures in the Bible that speak of cherubs and seraphim with wings; but these were more symbolic representations that prophets saw in visions rather than actual messengers from God. Throughout the ages artists based some of their paintings on these visions and thus perpetuated the belief that all angels have wings. Scriptures where actual messengers from God appeared to people do not mention any wings in their descriptions(Joseph Smith History 30-33, Dan. 8:15, Matt. 28:2, Mark 16:5).

Angels are all assigned to this earth and there have never been angels who have not or will not live on this earth(D&C 130:5). The following is a list of the types of angels who have served God and man:

1. There are spirit children of God who have not yet come to earth to gain a body (Abraham 3); this is probably the type of angel who appeared to Adam:

"And after many days an angel of the Lord appeared unto Adam, saying: Why dost thou offer sacrifices unto the Lord? And Adam said unto him: I know not, save the Lord commanded me."(Moses 5:6-8).

This type of being might also include angels of Satan who will never obtain a body. (2 Cor. 11:14-15; 2 Ne. 2:17)

2. There are the spirits of those who have died who are not yet resurrected. These are referred to as "the spirits of just men made perfect" (Heb. 12:22-23; D&C 76:69)
The singing angels at Christ's birth (Luke 2:9-14) were probably spirts of those who had died before He was born. They could not have been resurrected beings because Christ Had not been resurrected Himself yet.

3. There are those few who have been resurected since Christ and have as a result regained their body (D&C 129:1)
These would include angels who were instrumental in the restoration of the gospel such as Elias, Moroni, John the Baptist, Peter, James, and John. The angel Moroni, a resurrected being, revealed the record of the Book of Mormon to Joseph Smith. The bestowal of any ordinance or information from an angel that requires a physical interaction with a mortal requires that the angel posess a resurrected body.

4. There are a few others who once lived on this earth and were translated so that they shall "never taste of death"(3 Ne 28:7). Enoch and his people (Moses 7:18-21, 31, 63, 69; Heb. 11:5), Moses (Alma 45:19), Elijah (2 Kgs. 2:11-12), John the Revelator (Matthew 16:28), and three Nephites from the Book of Mormon (3 Nephi 28). were all translated beings. The translated prophets Elijah and Moses appeared as angels to Jesus and the Apostles (Matt. 17: 3) and later both appeared to Joseph Smith and Oliver Cowdery(D&C 110: 13-16) as resurrected beings(D&C 133: 55).

5. People who are living on the earth now can be called angels if they have been sent by God on a particular mission. An example of this are the three angels(holy men) who visited Abraham and Lot (JST Gen. 18 - 19).