Origin of the idea that "demons" and "fallen angels" are the same thing? Background

So I'm studying angels and demons right now, attempting to put together a picture of what the Bible teaches on these topics, and I'm struggling to find anything in the Bible that suggests that "demons" are the same thing as "fallen angels"! I'll admit that it would make things much simpler to explain if we could just assume that demons are fallen angels, but I need more to go off of than just convenience. :-) So I'm thinking the origin of this popular idea must be extra-biblical?

Question

Most of the sources I've come across simply assume that demons and fallen angels are the same thing. My question is why? Where does the idea come from that demons and fallen angels are the same thing? It is prevalent enough, but I can't find a source on it.

Failed Attempts

I came across a Catholic teaching on the topic, and they simply asserted it and cited verses where demons are mentioned... but none of the verses actually said anything about fallen angels. I came across a Catholic forum that ended in someone simply asserting that demons are by definition fallen angels... but I know people who believe they are different, so it can't simply be a dictionary definition thing. I've looked all over Scripture and the closest thing I can find is that Satan is in charge of demons and Satan is in charge of fallen angels... but that doesn't tell me that they're the same.

Difficulties to Address

The difficulty I'm having in simply assuming they are the same (besides not having a good reason to assume this) is that Scripture portrays angels -- and even Satan (a fallen angel) as spiritual beings that manifest as men, radient beings, etc., as if they're somewhat similar to people, but generally invisible to us. Demons, on the other hand, are portrayed as spirits that are extremely uncomfortable with being outside of a physical creature. When Jesus cast out a group of demons, they begged and pleaded with Him to at least let them go into the pigs nearby (etc.) I get the picture that demons are like internal parasites, whereas angels -- even fallen angels, are like people who walk, talk, etc. but have some differences like being invisible, extremely powerful, etc.

A Good Answer

I would welcome sound logical arguments from Scripture, but in the absence of such arguments, any historical background on when Christians began equating these two terms would be sufficient. Just wondering where the idea comes from, as I'm assuming it wasn't just an unfounded assumption that all the prominent Bible scholars now accept without question!
As close as I can understand these Scriptures they apply to the fallen Angels:


  Revelation 12:7 through 9 NKJV  And war broke out in heaven: Michael and his angels fought with the dragon; and the dragon and his angels fought, 8  but they did not prevail, nor was a place found for them in heaven any longer. 9  So the great dragon was cast out, that serpent of old, called the Devil and Satan, who deceives the whole world; he was cast to the earth, and his angels were cast out with him.


That does not say that those Angels are Demons, However; other Scriptures do lead us to understand they are:


  Luke 11:18 NKJV  If Satan also is divided against himself, how will his kingdom stand? Because you say I cast out demons by Beelzebub.


The Scriptures refer to Satan's helpers as both angels and demons:


  Matthew 25:41 NKJV  "Then He will also say to those on the left hand, 'Depart from Me, you cursed, into the everlasting fire prepared for the devil and his angels: 


compared to:


  Revelation 16:13 and 14 NKJV  And I saw three unclean spirits like frogs coming out of the mouth of the dragon, out of the mouth of the beast, and out of the mouth of the false prophet. 14  For they are spirits of demons, performing signs, which go out to the kings of the earth and of the whole world, to gather them to the battle of that great day of God Almighty.


Even though I cannot give you any verses which say that Demons are fallen Angels these Scriptures taken together along with the description of the Angel opening the gate to the bottomless pit leaves little doubt in my mind that they are the same. 

Hope this helps and sorry to not give you something more solid to use.