gotquestions.org is good, but for an apologetic of this magnitude (in which the Church will [most likely] never agree on an answer,) I prefer search the bible myself, reading context, Hebrew, Greek, and original translation (as best as I can find them.)
For if
God spared not the angels that sinned, but cast them down to hell, and delivered them into chains of darkness, to be reserved unto judgment;
And spared not the old world, but saved Noah the eighth person, a preacher of righteousness, bringing in the flood upon the world of the ungodly;
And turning the cities of Sodom and Gomorrha into ashes condemned them with an overthrow, making them an ensample unto those that after should live ungodly;
And delivered just Lot, vexed with the filthy conversation of the wicked:
(For that righteous man dwelling among them, in seeing and hearing, vexed his righteous soul from day to day with their unlawful deeds
The Lord knoweth how to deliver the godly out of temptations, and to reserve the unjust unto the day of judgment to be punished
2 Peter 2:4-9
The first verse says that the
angels that sinned are kept in chains until Judgment. They are not running around spiritually tormenting. They are in spiritual jail.
And the angels who did not keep their positions of authority but abandoned their proper dwelling—these he has kept in darkness, bound with everlasting chains for judgment on the great Day.
Jude 1:6
Again, the fallen angels that sinned (whether it meant trying to usurp God, or polluting the bloodline of His children by mingling seed) are
kept in darkness until judgment. That means they are not spiritually roaming around now as demons.
Now if the fallen angels (the fathers of the Gibborim/Rephaim/Anakim/Nephilim/etc.) have been kept in spiritual chains and will not be release until judgment and their doom, the deduction is that their offspring are these demons. Why?
If two humans (with dead spirits) mate, they produce a child with a dead spirit, which will eventually die in the flesh also. For example, Adam is the father of the human race, but his spirit died after he sinned (hence,
"this day you will die"; Gen. 2:17.) Therefore, if Adam mates with any other human with a dead spirit, he will produce a child dead in the spirit.
Christ was born of woman, but His Father is God - The Eternal Holy Spirit. Therefore, even though Christ's body was human, His Spirit was immortal (and vindicated as per His perfect life.) As a special case per His perfect life, Christ can even resurrect His mortal body to life - He is completely immortal.
Fallen Angels = spiritual beings/Immortals
Humans (post-Adam) = human beings/Mortals
An immortal being directly procreating with a mortal being will produce a mortal vessel with the spirit of the father. In the case of the Gibborim/Nephilim/Rephaim/Anakim, their father was an angel/pure spirit. Therefore, though these hybrids had "human" bodies (with genetic abnormalities like Giantism and polydigitism) which die, they have spirits of their father - which don't die unless God kills it.
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Now, notice there is a distinct difference between the Hebrew phrases
"b'nai Elohiym" in Gen 6:2, "
sa'iyr" in Lev 17:7, "
satan" throughout the old testament, and "
shed" in Deut 32:17, as well as the Hebrew word for a [good] angel:
B'nai Elohiym - Hebrew Phrase for Sons of God; colloquially called a Fallen Angel
Sa'iyr - Hebrew word for a Satyr, shaggy one, a he-goat, or devil ; colloquially called a devil
Satan - Hebrew word for an opponent, adversary, or arch-enemy of good; colloquially called satan
Shed - Hebrew word for
daemon; a devil. Colloquially called a devil
*
Malak* - Hebrew word for a dispatched deputy (of God,) or a messenger of God. Also used to describe a King, Teacher, Pastor, Ambassador, or Prophet (of God). Colloquially called an [Good] Angel
Demons in Hebrew is by definition NOT the same as any angel (b'nai Elohiym, Malak) - fallen or otherwise. We are given power by Christ
as humans to cast out devils, or "daimonions" in Greek (in His name.)
Daimonion - Greek word for a daemonic being.
Yet, we won't haven anything to do with the [fallen] angels until
judgment:
Dare any of you, having a matter against another, go to law before the unjust, and not before the saints?
Do ye not know that the saints shall judge the world? and if the world shall be judged by you, are ye unworthy to judge the smallest matters?
Know ye not that we shall judge angels? how much more things that pertain to this life?
1 Cor 6:1-3
So to bring it around, if the fallen angels are bound in spiritual chains until judgment, and the saints judge them at Judgment, then the angels are not the spirits existent as "satan," "shed," or "daimonion" on earth today.
Their offspring that die (but have spirits of their angelic fathers) are ethereally existent, and are described as "satan," and especially "shed or daimonion." These are the creatures we have power over, to cast out these creatures in other people. Christ did not give us power to judge the angels
yet: that is reserved for Judgment Day. Moreover, there are no "[fallen] angels" to cast out or judge, because the sinful angels are all bound until Judgment Day.
That is my $0.02 from my own study. There is more detail from the book of Enoch that directly classifies daemons and fallen angels as separate entities, but of course the book of Enoch is close to blasphemy to some. Still, the bible canon provides enough detail to make the distinction.