Other than the reality of the Godhead, existence is divided into two realms: vertical and horizontal. The horizontal realm is physical and measurable. Vertical is the rest.
Angels are beings existing in the vertical realm.
Satan is not a physical being. By these definitions, he is an angel.
See also
Was Satan a cherub?
I think existence is multi layered and we only know of two of them.
Look up, look down, look inward, look outward, look forwards, look backwards.. multi layered.
I don't think Satan is an Angel. I think he is a time and place.
He is death and the grave, the very opposite of Christ which is life and heaven.
Deu 30:19
I call heaven and earth to record this day against you,
that I have set before you life and death, blessing and cursing: therefore choose life, that both thou and thy seed may live:
We say, the angel of death, because he is the bringer of it. Just as Christ is the bringer of light.
The evening and the morning.
Perhaps these are the two cherubim that reside over the mercy seat.
One accuses and the other pardons.
it's a paradox.
Eph 3:14
For this cause I bow my knees unto the Father of our Lord Jesus Christ,
Eph 3:15
Of whom the whole family in heaven and earth is named,
Eph 3:16
That he would grant you, according to the riches of his glory, to be strengthened with might by his Spirit in the inner man;
Eph 3:17
That Christ may dwell in your hearts by faith; that ye, being rooted and grounded in love,
Eph 3:18
May be able to comprehend with all saints what
is the breadth, and length, and depth, and height;
Eph 3:19
And to know the love of Christ, which passeth knowledge, that ye might be filled with all the fulness of God.
So who gave Satan his name? The Father. Who gave Jesus Christ his name? The Father.
Who gives us names? Our parents.
We give our children names.
It's like a family tree.
Satan isn't a very good dad, so the Father took his children and gave them to Jesus Christ.
And we are passed from death unto life.
And he paid for us with his own blood.
There so many ways to consider everything.
I don't know if we'll ever fully understand it all.
But it sure is fun picking at it.
Hugs