I have always thought that demons were the fallen angels, but in Jude 6 it says:
 And the angels who did not keep their positions of authority but abandoned their own home—these he has kept in darkness, bound with everlasting chains for judgment on the great Day. (NIV)
So, I'm thinking I was wrong because it says they are bound - so, what are demons if they are not angels, or are they?
A: This is a great question. We have attempted to address most of the main theories for who or what demons are in a previous post on demons. Those interested in our best attempt to answer the question, "so, what are demons if they are not angels, or are they?" should go and read that previous post first.
I like to see your theological reasoning in play and that you are willing to assess your previous assumptions (in this case, that demons are fallen angels). We all bring presuppositions to the text of Scripture that influence our reading. Not all of these assumptions are valid! Nowhere in the biblical text, that I'm aware of, is an explicit reference made that says demons are fallen angels. However, this idea is firmly embedded in our culture. If you do make that assumption, there are several verses that sure seem to indicate demons are fallen angels.
If you've read through the previous post, you'll see that I do not take the position that demons are fallen angels. The reason that I came to that conclusion is based (in part) on what comes a few verses later in Jude 8-10. I'll admit, however, that this conclusion is speculative. Without the Bible being explicit, we must hold our theological conclusions lightly. We don't want to go beyond what is written and begin abusing each other and fighting over disputable matters in direct violation of the command of the Scriptures (1 Corinthians 4:6).
But is that what Jude 6 says?
The translation of this particular verse reads slightly differently if you compare translations, which is always a good study technique to alert you to difficulties or possible translational problems in the text. Digging into this verse a little bit will show that the reference to angels is modified by a descriptive relative clause: "the ones who did not keep their positions of authority but abandoned their own home." It's these specific angels just described whom God has "kept in darkness, bound with everlasting chains for judgment on the great Day."
One possible interpretation is that Jude is describing all angels who fell when he provides this relative clause about their abandoning their positions of authority. In fact, some would even point to this as a proof text that the angels rebelled against God and fell with Satan. If this is true, then your reasoning seems to hold a lot of weight. Since these rebellious angels were then bound with chains until Judgment Day they cannot be equated with the demons which Jesus and the Apostles were consistently confronting and casting out from people on the Earth.
A different possibility exists. Perhaps Jude is referring to a specific group of angels through this relative clause. If so, he is intending to point the reader of his letter to a smaller segment of the angel population. Not referring to all angels in general. If he meant all angels, he could have simply written: "And the [rebellious/fallen] angels ... He has kept in darkness, bound with everlasting chains for judgment on the great Day." Of course, basing doctrine on what the Scripture does not say (instead of what it does say) is usually bad practice.
Nonetheless, this modifying clause about the angels to which Jude is referring provides us with some important information. First of all, Jude expects that his original audience is at least familiar with the non-canonical Book of Enoch, which he quotes from in vv. 14-15 (a citation of 1 Enoch 1:9). This is significant because the book of Enoch makes use of an interpretation that identifies the angels who left their abode as the "sons of God" referred to in Genesis 6:4 who came to breed with the "daughters of men." The resulting race from this angelic/human mix eventually led to "the Watchers" (e.g. 1 Enoch 1:5) and what we would call today, "demons." This possibility was discussed briefly in our previous post on demons (the "second possibility" discussed).
If that's too speculative, we can at least understand from other passages that not all angels are created equal. Not all contain the same authority. Michael and Gabriel are the only two angels specifically named in the canonical Scriptures. These two angels have a special status and place amongst the angels. Over the centuries various attempts have been made to describe the "angelic hierarchy." One attempt by Dionysius the Areopagite, which was expanded and explained in great detail by Thomas Aquinas in his Summa, concluded that the angelic host could be broken up into three separate orders. Each with three divisions. This explained the descending levels of authority. Likewise, there are varying levels of authority in the demonic realm in this view.
Whether or not we accept the conclusions of these particular church fathers, the biblical text does seem to indicate that both kingdoms -- light and dark -- have hierarchy, authority, and structure. It's entirely possible, therefore, that the angels Jude is referring to are those who held a higher rank and authority (and abandoned that authority). Lesser ranking angels with no authority in the angelic host have fallen and become "demons" as we call them. Spiritual beings that live and act in the human realm until Judgment comes (Matthew 8:29).
We don't necessarily need to know what demons are or exactly how they got here. But we do need to know that they exist. We should be aware of their influence and doctrines (e.g. 1 Timothy 4:1). We can speculate and arrive at conclusions that are based on careful study of the Word of God and prayer. After that we must be careful not to be divisive over these conclusions. To be so is dishonoring to the Lord.
At the very least, we can be sure that at least some angels are currently held in chains awaiting judgment on the Day of the Lord. Jude intends for this to be an example to humans. Judgment is coming and no one who fails to believe in Jesus will be spared on that Day! Jude is not calling us to speculate about the origin of demons but to live soberly in the light of this truth that God is both just and the justifier of the one who has faith in Jesus (Romans 3:9-31). Jude is bringing all of this up because the believers to whom he was writing were failing to remain diligent in contending for the truth of the faith. They were allowing false teaching to creep in. This was destructive (Jude 3-4) because it led to people denying Jesus - a catastrophic error.
Let us live in the light of the truth. Jesus Christ is coming. He is the only King and Savior. As King, He commands that all confess their sin and rebellion against Him, confess that they are deserving of His condemnation as a result, turn to Him through repentance of their rebellion and in loyalty bow their knee to Him as King, and trust fully in Him and His work on the cross for the pardon of their sin. There is no other Name given to men by which we may be saved from the just wrath that is to come! Thanks be to God for His mercy and grace through Jesus Christ our Lord!