Are fallen angels the same as demons? Are the fallen angels bound up in chains?

Let me try and give a brief answer to your question. You will notice that I use the King James "devils" instead of the transliteration "demon." I am not criticizing, just staying with the biblical terminology. Also, I admit that the distinctions that I am getting ready to give you are not agreed upon. They are my best conclusions according to the Bible. The spiritual beings that are in opposition to God include:

1. The Devil
2. The fallen angels that actively serve the devil at this time. These are ye to be cast out (Revelation 12:9And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and his angels were cast out with him.
   See All...).
3. The fallen angels that are presently in chains (2Peter 2:4For 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;
   See All...; Jude 1:6And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day.
   See All...). These are a special group of fallen angels who are given to greater judgment. They "kept not their first estate" (2Peter 2:4For 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;
   See All...). That is, they did not keep their home in heaven. They seem to be connected with the destruction of the world in Noah's day (2Peter 2:4-5 [4] 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; [5] 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;
   See All...). I believe this identifies them as the sons of God who came down and married with the daughters of men in Genesis 6:1-4 [1] And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them, [2] That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose. [3] And the LORD said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years. [4] There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.
   See All.... Because of their perversion in seeking the daughters of men, they received a greater and more immediate punishment for their sins.
4. The devils. The devils are never called fallen angels. They have attributes that are never attributed to angels. The most significant attribute is their desire to inhabit a body (Matthew 8:28-31 [28] And when he was come to the other side into the country of the Gergesenes, there met him two possessed with devils, coming out of the tombs, exceeding fierce, so that no man might pass by that way. [29] And, behold, they cried out, saying, What have we to do with thee, Jesus, thou Son of God? art thou come hither to torment us before the time? [30] And there was a good way off from them an herd of many swine feeding. [31] So the devils besought him, saying, If thou cast us out, suffer us to go away into the herd of swine.
   See All...). Though angels can take on a body of flesh, they have no need to do so because they are created as spirits (Hebrews 1:14Are they not all ministering spirits, sent forth to minister for them who shall be heirs of salvation?
   See All...) and are complete in that form. The devils are spirits too, being called evil spirits (Luke 7:21And in that same hour he cured many of their infirmities and plagues, and of evil spirits; and unto many that were blind he gave sight.
   See All...). But they are not complete in spirit form. They are continually seeking out a body to indwell. Matthew 12:43-45 [43] When the unclean spirit is gone out of a man, he walketh through dry places, seeking rest, and findeth none. [44] Then he saith, I will return into my house from whence I came out; and when he is come, he findeth it empty, swept, and garnished. [45] Then goeth he, and taketh with himself seven other spirits more wicked than himself, and they enter in and dwell there: and the last state of that man is worse than the first. Even so shall it be also unto this wicked generation.
   See All... tells of the search of an unclean spirit for a body to inhabit. This type of language is never used with angels.

Of course, if devils are not fallen angels, the question arises as to who they are. The logical answer would be that they were beings that once had bodies since they now seek to inhabit one. My guess (and it is a guess) is that they are spirits of earlier inhabitants of an earlier earth (not men) who rebelled against God and are awaiting judgment--they feared that Christ was come to torment them "before the time" (Matthew 8:29And, behold, they cried out, saying, What have we to do with thee, Jesus, thou Son of God? art thou come hither to torment us before the time?
See All...).

That there should be spirit beings in many forms and at many levels should not surprise us. Ephesians 6:12For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places.
See All... states, "For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places."