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.