This is the text of an answer I posted to a similar question on Christianity SE:
From the perspective of the Greek New Testament, demon could be said to represent δαίμων (daimōn, from which the corresponding English word is derived) and devil could be said to represent διάβολος (diabolos; viz. "diabolical"). A variant of the word δαίμων - δαιμόνιον (daimonion) - is more often used.
Daimon and daimonion together appear 82 times in Scripture (17 times in the Septuagint, 65 in the New Testament). Diabolos appears 60 times (22 times in the Septuagint, 38 in the New Testament).
The word diabolos can also mean "slanderer", as in:
Esther 8:1 LXX
Καὶ ἐν αὐτῇ τῇ ἡμέρᾳ ὁ βασιλεὺς Ἀρταξέρξης ἐδωρήσατο Εσθηρ ὅσα ὑπῆρχεν Αμαν τῷ διαβόλῳ
And in that day king Artaxerxes gave to Esther all that belonged to Aman the slanderer
In the "diabolical" sense it seems always to refer to a single individual - the devil. In the Septuagint, for example, Job refers continually to ό διάβολος (the devil). This is also the case in the New Testament:
Τότε ὁ Ἰησοῦς ἀνήχθη εἰς τὴν ἔρημον ὑπὸ τοῦ Πνεύματος πειρασθῆναι ὑπὸ τοῦ διαβόλου
Then Jesus was led up by the Spirit into the wilderness to be tempted by the devil.
Ἰησοῦν τὸν ἀπὸ Ναζαρέτ, ὡς ἔχρισεν αὐτὸν ὁ Θεὸς Πνεύματι Ἁγίῳ καὶ δυνάμει, ὃς διῆλθεν εὐεργετῶν καὶ ἰώμενος πάντας τοὺς καταδυναστευομένους ὑπὸ τοῦ διαβόλου
how God anointed Jesus of Nazareth with the Holy Spirit and with power; how he went about doing good and healing all that were oppressed by the devil
μηδὲ δίδοτε τόπον τῷ διαβόλῳ
and give no opportunity to the devil.
Daimon and daimonion, on the other hand, are almost always used in the plural, and when not, the context implies that the word refers to one of many. For example:
ἀσθενοῦντας θεραπεύετε, λεπροὺς καθαρίζετε, νεκροὺς ἐγείρετε, δαιμόνια ἐκβάλλετε·
Heal the sick, raise the dead, cleanse lepers, cast out demons.
ἄλλοι ἔλεγον· ταῦτα τὰ ῥήματα οὐκ ἔστι δαιμονιζομένου· μὴ δαιμόνιον δύναται τυφλῶν ὀφθαλμοὺς ἀνοίγειν;
Others said, “These are not the sayings of one who has a demon. Can a demon open the eyes of the blind?”
σὺ πιστεύεις ὅτι ὁ Θεὸς εἷς ἐστι· καλῶς ποιεῖς· καὶ τὰ δαιμόνια πιστεύουσι καὶ φρίσσουσι.
You believe that God is one; you do well. Even the demons believe — and shudder.
In the Septuagint, diabolos translates the Hebrew שָׂטָן (śā·ṭān) - obviously the origin of our English word, "Satan". On 36 occasions, the New Testament transliterates שָׂטָן into Greek (Σατανᾶς - Satanas); as in:
ὁ δὲ στραφεὶς εἶπε τῷ Πέτρῳ· ὕπαγε ὀπίσω μου, σατανᾶ·
But he turned and said to Peter, “Get behind me, Satan!"
In the Septuagint daimonion often translates שֵׁד (šēḏ), which means "evil spirit" - usually of the sort that is worshipped as a god.
Ambiguity between the two terms is in the English language, but not necessarily the Greek or Hebrew Scriptures. The Concise Oxford English Dictionary defines demon as "an evil spirit or devil" and devil as "an evil spirit; a demon". Some English Bible translations use the two terms somewhat interchangeably. The King James Bible, for example, translates all three Greek words (diabolos, daimon, daimonion) as "devil". The RSV (and I presume the Catholic Edition RSV), on the other hand, seems to preserve the distinction and translate(s) diabolos as "devil" and daimon/daimonion as "demon".
The origin of and distinction between the devil (diabolos) and demons (daimonia) according to first millennium Chalcedonian Christian theology is explained in John of Damascus' (676-749) The Exact Exposition of the Orthodox Faith in Book II, ch.4, "Concerning the devil and demons", written sometime in the early 8th (or perhaps late 7th) century:
He who from among these angelic powers was set over the earthly realm, and into whose hands God committed the guardianship of the earth, was not made wicked in nature but was good, and made for good ends, and received from his Creator no trace whatever of evil in himself. But he did not sustain the brightness and the honour which the Creator had bestowed on him, and of his free choice was changed from what was in harmony to what was at variance with his nature, and became roused against God Who created him, and determined to rise in rebellion against Him: and he was the first to depart from good and become evil. For evil is nothing else than absence of goodness, just as darkness also is absence of light. For goodness is the light of the mind, and, similarly, evil is the darkness of the mind. Light, therefore, being the work of the Creator and being made good (for God saw all that He made, and behold they were exceeding good) produced darkness at His free-will. But along with him an innumerable host of angels subject to him were torn away and followed him and shared in his fall. Wherefore, being of the same nature as the angels, they became wicked, turning away at their own free choice from good to evil.
(John of Damascus is considered a "Doctor of the Church" by the Roman Catholic Church and an authoritative Church Father by Eastern Orthodox).
The Scriptural basis for these beliefs is summarized in one Orthodox dogmatic theology:
According to the testimony of the word of God, the origin of sin comes from the devil: He that committeth sin is of the devil; for the devil sinneth from the beginning (I John 3: 8). The word “devil” means “slanderer.” Bringing together the evidence of Sacred Scripture, we see that the devil is one of the rational spirits or angels who deviated into the path of evil. Possessing, like all rational creatures, the freedom which was given him for becoming perfect in the good, he “abode not in the truth” and fell away from God. The Saviour said of him: He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar and the father of it (John 8: 44). He drew the other angels after himself into the fall. In the epistles of the Apostle Jude and the Apostle Peter, we read of the angels which kept not their first estate, but left their own habitation (Jude, v. 6; compare with II Peter 2: 4).*
* M. Pomazanski, Orthodox Dogmatic Theology (3rd ed.; St. Herman of Alaska Brotherhood, 2005), p.153