What are the different types of angels?"
Answer: Angels fall into two categories: the "unfallen" angels and the fallen angels. Unfallen angels are those who have remained holy throughout their existence and accordingly are called "holy angels." In Scripture, generally when angels are mentioned, it is the class of holy angels in view. By contrast, the fallen angels are those who have not maintained their holiness.
Holy angels fall into special classes, and certain individuals are named and mentioned. Michael the archangel is likely the head of all the holy angels, and his name means "who is like unto God?" (Daniel 10:21; 12:1; 1 Thessalonians 4:16; Jude 1:9; Revelation 12:7-10). Gabriel is one of the principal messengers of God, his name meaning "hero of God," and was entrusted with important messages such as those delivered to Daniel (Daniel 8:16; 9:21), to Zechariah (Luke 1:18-19), and to Mary (Luke 1:26-38).
Most holy angels are not named in the Bible but are described only as "elect angels" (1 Timothy 5:21). The expressions "principalities" and "powers" seem to be used of all angels whether fallen or holy (Luke 21:26; Romans 8:38; Ephesians 1:21; 3:10; Colossians 1:16; 2:10, 15; 1 Peter 3:22). Some angels are designated as "cherubim," which are living creatures who defend God's holiness from any defilement of sin (Genesis 3:24; Exodus 25:18, 20). "Seraphim" are another class of angels, mentioned only once in Scripture in Isaiah 6:2-7, and are described as having three pairs of wings. They apparently have the function of praising God, being God's messengers to earth, and are especially concerned with the holiness of God. Most of the references to holy angels in Scripture refer to their ministries, which are broad. Holy angels were present at creation, the giving of the Law, the birth of Christ and His resurrection, the Ascension, and they will be present at the rapture of the Church and the second coming of Christ.
In stark contrast to the company of holy angels, the fallen angels are also innumerable, though considerably less than the holy angels, and are described as fallen from their first estate. Led by Satan, who was originally a holy angel, the fallen angels defected, rebelled against God, and became sinful in their nature and work. Fallen angels have been divided into two classes: those who are free and those who are bound. Of the fallen angels, Satan alone is given particular mention in the Bible. When Satan fell (John 8:44; Luke 10:18), he drew after him one third of the angels. Of those, some are reserved in chains awaiting judgment (1 Corinthians 6:3; 2 Peter 2:4; Jude 1:6), and the remainder are free and are the demons, or devils, to whom reference is made throughout the New Testament (Mark 5:9, 15; Luke 8:30; 1 Timothy 4:1). They are Satan's servants in all his undertakings and share his doom (Matthew 25:41; Revelation 20:10).
Recommended Resources: Angels: Elect & Evil by C. Fred Dickason and Logos Bible Software.