The Greek words for "demon" (daimonion), "devil" (diabolos), and "Satan" (satanas) have taken a very different meaning today than it had in Christ's time. Only one of these words, the Greek word usually translated as "demons", clearly has a different meaning in traditional Greek than its use in the Gospels.
More importantly, all three of these words have been changed and been conflated by subsequent religious teaching. Part of the reason for this, however, it that the different gospel writers used all these different terms in parallel verses, for example in describing the seeds by the wayside, Matthew 13:19 uses "the evil one", Mar 4:15 uses "satan", and Luke 8:12 uses "the devil".
This article looks at the meaning of these words in the Greek and in Christ's usage of them.
The current idea of "the devil" comes from conflating several different concepts (“demons”, “devils”, and “satan”) that Christ used to explain different aspects of life’s adversities. Loosely translated these concepts describe our personal demons (useless ideas in our heads), those who try to tear down others (useless members of society), and people who oppose others doing the right thing.
The Greek Words
First, let use define the Greek words involved. First, we have daimonion (δαιμόνια), which is usually translated as "demon" but which also gets translated as "devil." It actually means in traditional Greek "divinity", "divine power", and a "lower divine being". It was not a negative word in Greek, but we will look how Christ uses it and why later in this article. Christ uses this word about a dozen times.
The next Greek word is diabolos (διάβολος), which is consistently translated as "devil". It means "slanderous", "backbiting," and "slanderer." It doesn't mean a spirit, but it is clearly negative. Christ uses it only four times in a way consistent with the Greek (Mat 13:3, Mat 25:41, Luke 8:12 and Jhn 8:44).
Finally, we have "Satan" (Σατανᾶς), which is from the word satanas which is an Aramaic and Hebrew word meaning "adversary", "opponents," or "one who opposes another in purpose or act." It is neither a positive or negative word depending on who or what is opposed. Christ uses it only a handful of time but he uses it consistent with its Greek meaning, but always negatively.
Notice, none of these words have the same meaning. All of their meanings are very specific and they don't really overlap. The confusion starts with Biblical translation, which often translates the first word as "devil" as well as "demon". Christ does use "Satan" in the context of discussing "demons" but he does so in a way that clarifies his meaning in using "demon", not to confuse the meaning of the terms.
Driving Out "Demons"
Th Greek word daimonion does not mean "demon" as an "evil spirit", much less the "devil" in Greek. The Greek word means "divinity", "divine power", "a lower divine being." It is not a negative term. Quite the opposite. As an adjective, it meant "miraculous", and "marvelous", not "demonic". It was used as a term of address as an honorific, "good lady" or "good sir". On the spiritual side, it refers to "visitations of heaven" and the "ways of the gods". As a verb, it meant "to be possessed by a god".
However, this is clearly not the way that Christ uses it nor the way that the people in Judea in his era used the word. Christ uses it to refer to "spirits," that is, to things that exist in a non-material way. Christ uses the Greek word for "spirit" (pneuma) in the same context as daimonion. For example, in Mat 12:27, he uses daimonion at the beginning of a discussion about casting out demons, but as he continues to talk about what happens when a demon is cast in Mat 12:43 and Mat 12:45 which uses pneuma, for "spirit". Pneuma means "blast", "wind", "breath", "the breath of life," and "divine inspiration", that is,. Christ used this word to describe both God, and "demons". So pneuma is a non-material form of life, "non-material" power. It is the "voice" of conscious thought.
Christ is often described by the Gospel writers as "casting out devils" but he only uses the word daimonion translated variously as "devil", "evil spirit," or "demon", less than a dozen times himself. (Mat 7:22, Mat 10:8, Mat 11:18, Mat 12:27 Mat 12:28 Mat 12:43, Mar 7:29, Mar 16:17, Luk 11:18,Luk 11:19,Luk 11:20, Luk 13:32, Jhn 8:49) More interestingly, he almost always uses it in the context of describing a specific ability, the ability of "casting out devils". He actually defends himself from the accusation of being possessed by a demon in Jhn 8:49.
Of course, we talk about people fighting against their internal demons today. But we do this in the context of discussing mental disorders. If the Christ story was being written today, it would be filled with stories referring to people with "addictions", "troubled minds", "schizophrenia", "mental disorders," and, especially, "delusions." The terms would be more psychological because we view our society as more scientific. However, the real delusion here is that we have a better and more honest understanding of the human mind and the human spirit today than people did two thousand years ago. What we really have is a new way of talking about what we don't understand. Our pretense of understanding is done in different terms that the pretense of understanding in Christ's era.
A more interesting question is how did the positive Greek idea of daimonion become the negative idea of a mental disorder in Christ's time? Remember, the verb form of this term means "to be possessed by a god". To the Jews, the Greek "gods" were false, false ideas, delusions. Being possessed by them was to be deluded. From that small step, the term became a general term for mental disorders. Remember, they didn't have our "scientific" vocabulary for these ideas. Our information technology also gives us ways of thinking about the power of logic outside of the context of conscious thought.
The term "Beelzebub" is used to describe the master of demons (Mat 12:27). The word is a Hebrew play on words. The term"Ba'al Zebub" ("Lord of the Flies" or "Lord of the Flyers") is a Hebrew pun on "Ba'al Zebul" meaning "Lord of the Manor". Christ's concept of "demons" is that they move through the mind and ideas, not through the physical world. Therefore, they are "flyers". God's messengers may be another type of "flyer". Interestingly, Christ use the term "flyer" to describe birds, rather than the Greek term for "bird".
People of the ancient world accepted that power could exist apart from the material world, especially the power of thought. Living spirits, pneuma, apart from the body were an accepted phenomena. This was the standard explanation for addiction, mental illness, and delusions that afflicted people. An argument can be made that Christ saw the word "demons" as what we would call "disabilities", that is, having a lack of power over something. In Mat 7:22, Christ contrasts "demons" as disabilities against the "power" of abilities.
Christ use of these terms for various mental delusions was in response to others who used these terms. He actually explained why "wind," the literal meaning of the Greek pnuema, symbolizes "spirit" in Jhn 3:8. He uses the Greek terms "spirit", and "demon," to respond to people who used these same terms to describe the afflictions that they saw. In other words, Christ is using their own terms to talk to people about how the world as they described it. In using their terms, he wasn't endorsing those terms or their world-view as much as he communicating in the language of the people.
"Devil" as Slanderers and Degraders
The word translated as "devil" (diabolos) is the simplest term here and it is used the least frequently. As explained above it means "slanderous", "backbiting," and "slanderer." The Greek word diabolos is the source of the English word "devil" in the sense of a person who degrades or attempts to degrade another person. Christ uses this term in Mat 13:3, Mat 25:41, Luke 8:12 and John 8:44.
Christ's clearest statement regarding his use of the term is John 8:44. In it, he says, literally, "You are from the father of yours, the slanderer and wish to create the desires of your father. That one was a man-killer from the start as he didn't keep with the truth. This is because the truth is not in him. When you tell lies, he has spoken from his own. This is because he is a liar and the father of the same." So the "devil" is a "man killer", but what is a "man killer". Christ seems to mean someone who destroys people's reputations because "he doesn't keep with the truth." The focus is on lying and encouraging others to lie as "the father of lies".
In Mat 25:41, Christ describes the "eternal fire" (see this article on the meaning of fire) as being created for the "devil" and "his angels", but the word for "angels" actually is the Greek word meaning "messengers."
Part of the confusion about the "devil", "satan", and even "demons" is that the Gospel writers (Matthew and Luke) use this term to describe the person who tempts Christ during his forty days in the desert. Though we do not have Christ's words describing this event, we know that it could have only come from his recounting it because he was the only one there. During the encounter, the term "devil" certainly applies, since the tempter seeks to get Christ to degrade himself, but at the end of the encounter, Christ addresses his tempter as "Satan", but he doesn't use this as a name (see below). It is simply as a description, "adversary". Since this story is clearly about a spiritual being (or one that inhabits the mind), the term "demon" also apply to the tempter, though Christ doesn't use that term any more than he uses the term "devil".
In Christ's use of the term diabolos makes it clear that this person is "evil" or, more precisely "worthless". In Luke 8:12, Christ uses the term to describe the force that snatches his ideas from someone's heart (parable of the sower). However in Mat 13:19, the parallel text, another word is used, "the worthless one" from the Greek poneros, which means "burdened by toil", "useless," and "worthless." In a moral sense, it means "worthless", "base," and "cowardly." (See this article on Greek words used to express "evil" and "good"). Interestingly, Matthew does use diabolos is the explanation of the parable that follows "the parable of the sower", "the parable of the weeds". Luke does not recount this parable but it seems possible that a term from one made its way to the other in someone's memory of the explanations.
"Satan" as Adversity
Our word "Satan" is from the Greek form satanas from a Hebrew satan ( שטן) meaning "adversary", "opponent," or "one who opposes another in purpose or act. " The Greek version of this word appears initially only in the New Testament. Interestingly, the Greek Septuagint actually translates the Hebrew word satan into the Greek word diabolos, which means "slanderer".
The meaning that Satan has today as the name of "the chief of evil spirits" comes from Christian traditions unknown at the time the Gospels were written. The Hebrew word was not a name, but a descriptive noun. King David is described as an adversary of his enemies with the term "satan." Even in the story of Job, where the adversary is personalized, the Hebrew "satan" is never used as a name, since it is used with a definite article ("the"), which Hebrew never does with proper names, "the adversary". More about the meaning of the Hebrew word from the Old Testament in this Bible Topics article.
In the Hebrew sense, "satan" means "an adversary" or more generally, "adversity" in the sense of "life's adversity" and, even more, "the accuser" in the sense of our inner voice of self-doubt.
Christ uses the word only three times in Matthew (Mat 4:10 Begone, Satan! for it is written, 'You shall worship the Lord your God..., Mat 12:26 And if Satan casts out Satan, Mat 16:23 Get behind me, Satan). While he uses it to address someone twice, he does not use it as a name. This is an artifact of poor translation. In the Greek, the word is clearly not in the form of an address (called vocative) but in the form of an object of the verb. In other words, Christ is describing these people as an adversary, not calling them a name. The sense in the Greek in Mat 4:10 is not "go away, Satan" but more like "take away adversity" or "take away a barrier."
So despite capturing different ideas, these three Greek words are best understood and discussed in terms of how Christ uses them. Though Christ may have used these terms to describe aspects of a spiritual being that Christian teaching calls "Satan, the devil", these terms were not used as names or titles of such a being. The term daimonion was much more commonly used both by Christ and the Gospel writers, but it was used as a term of art to describe what we describe today as "mental disorders".
A more basic problem here comes from of the word translated as “sin” and “evil”. Those words means “mistake” and “worthless”. See this article on those concepts.