Are there classes of angels?

Yes. Michael the archangel is very powerful and the angel Gabriel is a high-ranking angel, a messenger. Jude 1:9 shows that Michael has always possessed great power and influence. According to Strong's Concordance #743, the word archangel comes from the Greek word archaggelos and means a chief angel. The archangel Michael powerfully leads good angels in battle against evil:

"And war broke out in heaven:  Michael and his angels fought with the dragon; and the dragon and his angels fought, but they did not prevail, nor was a place found for them in heaven any longer" (Revelation 12:7-8).

The angel Gabriel undertook important tasks. He appeared to the prophet Daniel to interpret a vision (Daniel 8:15). He gave Daniel a prophecy recorded in Daniel 9:20 and Luke 1:19. Gabriel announced the birth of John the Baptist to Zechariah. In Luke 1:26, God sent Gabriel to Nazareth in Galilee to Mary to tell her that she is with child by the Holy Spirit. He also announced the birth of Jesus.

There are cherubim, but we do not know their names or their ranking. We only know that the four living creatures are cherubim (Ezekiel 10:19-20).