What are the differences between cherubim and seraphim?

This article Cherubim | New Advent says that Pope St. Gregory I ("the Great") divided the nine angelic orders into three choirs, and those in the highest choir listed in ascending order being: thrones, cherubim, and seraphim. the Pope then said chreubim means "the fulness of knowledge".

Pope Gregory divided the nine angelic orders into three choirs, the highest choir being: thrones, cherubim, and seraphim. Of the cherubim he says (Hom. in Ev., xxxiv, 10), that cherubim means "the fulness of knowledge, and these most sublime hosts are thus called, because they are filled with a knowledge which is the more perfect as they are allowed to behold the glory of God more closely".

This article Seraphim | New Advent differentiates cherubim and seraphim as follows:

They are distinct from the cherubim who carry or veil God, and show the presence of His glory in the earthly sanctuary, whilst the seraphim stand before God as ministering servants in the heavenly court. Their name too, seraphim, distinguishes them from the cherubim, although it is confessedly difficult to obtain from the single Scriptural passage wherein these beings are mentioned a clear conception of its precise meaning.

It appears that the quotation above and the one that follows below that the precise meaning is not readily obtainable from scripture.¹

The name is oftentimes derived from the Hebrew verb saraph ("to consume with fire"), and this etymology is very probable because of its accordance with Isaiah 6:6, where one of the seraphim is represented as carrying celestial fire from the altar to purify the Prophet's lips.

The article then goes on to say where seraphim is mentioned in scripture and what they are represented as doing.

The seraphim are mentioned at least twice in the Book of Enoch (lxi, 10; lxxi, 7), together with and distinctly from the cherubim. In Christian theology, the seraphim occupy with the cherubim the highest rank in the celestial hierarchy, while in the liturgy (Te Deum; Preface of the Mass) they are represented as repeating the Trisagion exactly as in Isaiah 6.

<sup>Footnote
1. It is interesting to note that St. Thomas in this article: Summa Theologica > First Part > Question 63 | New Advent, states "Seraphim" means "those who are on fire," and [...] Seraphim is derived from the heat of charity[.]</sup>

Endnotes

1. cf. CHERUB | Jewish Encyclopedia and SERAPHIM | Jewish Encyclopedia.

Before answering your question, I must thank you for several hours of some very interesting and informing research.

It appears from what I am able to determine that Cherubim are The angels we are most accustomed to envision when we hear the word Angel.

Genesis 3:24 So he drove out the man; and he placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life.

כּרוּב kerûb him him him BDB Definition:

1) cherub, cherubim (plural)

1a) an angelic being

1a1) as guardians of Eden

1a2) as flanking God’s throne

1a3) as an image form hovering over the Ark of the Covenant

1a4) as the chariot of Jehovah (figuratively)

Part of Speech: noun masculine

A Related Word by BDB/Strong’s Number: of uncertain derivation

However, the word Angel has a different definition:

מלאך mal'âk

BDB Definition:

1) messenger, representative

1a) messenger

1b) angel

1c) the theophanic angel

Part of Speech: noun masculine

A Related Word by BDB/Strong’s Number: from an unused root meaning to despatch as a deputy

There are two descriptions of Cherubim in the Bible and they differ in the following Scriptures:

Exodus 25:20 And the cherubims shall stretch forth their wings on high, covering the mercy seat with their wings, and their faces shall look one to another; toward the mercy seat shall the faces of the cherubims be.

This description would lead us to believe that these Cherubims only have one face and there is no mention of any fire or wheels, as in Ezekiel’s description

Ezekiel 10:1 through 20 Then I looked, and, behold, in the firmament that was above the head of the cherubims there appeared over them as it were a sapphire stone, as the appearance of the likeness of a throne. And he spake unto the man clothed with linen, and said, Go in between the wheels, even under the cherub, and fill thine hand with coals of fire from between the cherubims, and scatter them over the city. And he went in in my sight. Now the cherubims stood on the right side of the house, when the man went in; and the cloud filled the inner court. And the sound of the cherubims' wings was heard even to the outer court, as the voice of the Almighty God when he speaketh. And it came to pass, that when he had commanded the man clothed with linen, saying, Take fire from between the wheels, from between the cherubims; then he went in, and stood beside the wheels. And one cherub stretched forth his hand from between the cherubims unto the fire that was between the cherubims, and took thereof, and put it into the hands of him that was clothed with linen: who took it, and went out. And there appeared in the cherubims the form of a man's hand under their wings. And when I looked, behold the four wheels by the cherubims, one wheel by one cherub, and another wheel by another cherub: and the appearance of the wheels was as the colour of a beryl stone. And the cherubims were lifted up. This is the living creature that I saw by the river of Chebar. And when the cherubims went, the wheels went by them: and when the cherubims lifted up their wings to mount up from the earth, the same wheels also turned not from beside them. Then the glory of the LORD departed from off the threshold of the house, and stood over the cherubims. And the cherubims lifted up their wings, and mounted up from the earth in my sight: when they went out, the wheels also were beside them, and every one stood at the door of the east gate of the LORD'S house; and the glory of the God of Israel was over them above. This is the living creature that I saw under the God of Israel by the river of Chebar; and I knew that they were the cherubims.

Again in Ezekiel he speaks of Cherubim, and attaches the wheels to them.

Ezekiel 11:22 Then did the cherubims lift up their wings, and the wheels beside them; and the glory of the God of Israel was over them above.

And in Ezekiel chapter 41 he describes some representations of Cherubim but these have two faces:

Ezekiel 41:18 and 19 And it was made with cherubim and palm trees, a palm tree between cherub and cherub. Each cherub had two faces, so that the face of a man was toward a palm tree on one side, and the face of a young lion toward a palm tree on the other side; thus it was made throughout the temple all around.

Whether or not this indicates that there are different forms of Angels, or not is not clear.

Seraphims appear to be a separate creation by God with a specific mission of continually praising God. The word translated Seraphim is שׂרף and has two definitions of the same word the only difference that I see between the two is in the pronunciation.

שׂרף śârâph

BDB Definition:

1) serpent, fiery serpent

1a) poisonous serpent (fiery from burning effect of poison)

2) seraph, seraphim

2a) majestic beings with 6 wings, human hands or voices in attendance upon God

Part of Speech: noun masculine

A Related Word by BDB/Strong’s Number: from H8313

שׂרף śâraph

BDB Definition:

1) to burn

1a) (Qal) to burn

1b) (Niphal) to be burned

1c) (Piel) burner, burning (participle)

1d) (Pual) to be burnt up, be burned

Part of Speech: verb

A Related Word by BDB/Strong’s Number: a primitive root

The word Seraphims only appears in the book of Isaiah:

Isaiah 6:1 through 3 In the year that king Uzziah died I saw also the Lord sitting upon a throne, high and lifted up, and his train filled the temple. Above it stood the Seraphims: each one had six wings; with twain he covered his face, and with twain he covered his feet, and with twain he did fly. And one cried unto another, and said, Holy, holy, holy, is the LORD of hosts: the whole earth is full of his glory.

All Scripture is quoted from The protestant translations of the Bible.

The best biblical description of cherubim (sing cherub) is to be found in the story of the Ark of the Covenant, and it appears that they were sphinx-like creatures with human heads, the bodies of lions and two wings. Similar figures appear throughout the ancient Near East, including, of course, Egypt. A Late Bronze Age representation appears on an ivory panel from Megiddo, as well as some Early Iron Age terra-cotta fragments that appear to have been part of cherub-thrones, providing evidence of continuity into the Israelite period.

Seraphim are described in Isaiah 6:2 as part of God’s retinue and it seems they were creatures of fire, with six wings. Isaiah does not identify the seraphim with angels. The Hebrew name, śārāf means 'the one that burns’, and is the same word as used for the black-necked cobra (see Numbers 21:6-9 and Deuteronomy 8:15), which applies its poison not only by biting but also by spitting. Othmar Keel and Christoph Uehlinger describe four-winged seraphim (cobras) found on Judahite name-seals, in Gods, Goddesses, and Images of God: In Ancient Israel, page 273, and say that the six wings in Isaiah 6 signify an increase in potency.

The Catholic Church is more concerned with identifying orders of angels than most other Christian denominations. Uta Ranke-Heinemann lists seraphim, cherubim, thrones, dominations, virtues, powers, principalities, archangels, and (lowest of all) simple ‘angels’, in Putting Away Childish Things, pages 55-56.

Strictly Biblically speaking, the Seraphim are only described once in the Bible:

In the year that King Uzziah died, I saw the Lord, high and exalted, seated on a throne; and the train of his robe filled the temple. Above him were seraphim, each with six wings: With two wings they covered their faces, with two they covered their feet, and with two they were flying. And they were calling to one another:

“Holy, holy, holy is the Lord Almighty;
the whole earth is full of his glory.”

At the sound of their voices the doorposts and thresholds shook and the temple was filled with smoke.
Isaiah 6:1-4

There really is not much about them. They have six wings and it seems that most of their purpose for existing is to sing praises to God in God's presence. The "doorposts and thresholds shook" at the sound of their voices. These are awesome creatures. No wonder Isaiah was terrified.

Cherubim on the other hand seem to be more simple, having only one set of wings. They are your typical angels and are described in a number of places in the Bible. They appear to look like people with wings. There's a good deal of information on them pretty much everywhere, so I'll neglect to expand on that. It seems their primary purpose for existence is to deliver messages from God to creation, and some suspect from creation to God as well. They also seem to have some multipurpose as soldiers. An example would be the destruction of Sodom and Gomorrah.

Outside of the 66 book Protestant canon there is a lot more information. Tons more. Outside of Christianity there is even more. Much too much for a single answer on this site. FMS's answer hints on some of it.