(Satan enthroned as the pope of hell, from Pierre Boaistuau's Histoires prodigieuses, 1597)
In our modern Western culture no distinction is usually made between the Devil, Satan and Lucifer. They are different aspects of one being. Even so, it can be useful to draw a distinction between them, since it helps define the complete nature of the ruler of hell, as shaped in the folklore of European Christians over the past thousand years and more.
Devil is from the Greek diaballein, to slander, or throw across. Hence the Devil is the great deceiver who throws obstacles across the path of humanity. Lucifer is Latin for light-bringing or light-bearing. This is said to have been the name of the leader of the angels who revolted against God in heaven, and were cast down into the pit as punishment for their desire to be independent. It is also the name of Venus when this planet rises in the east as the Morning Star. Lucifer was the name of the Devil while he was still an angel in heaven, but after his expulsion he became known as Satan, a Hebrew word that means enemy or adversary. Satan is the adversary of God, and if humanity is assumed to be obedient to God, he is the foe of mankind as well.
The modern stereotype of Satan is a humanoid male figure with two short curved horns on the top of his head (the two horns of the lamb, mentioned in Revelation 13:11 in connection with the second Beast). Either he is bald or has short black hair, usually accompanied by a goatee beard (because the goat is considered a Satanic beast). In more explicit depictions he is overtly masculine, with a muscular body and a large penis that may be sharply pointed and horn-shaped, but his male organ is often covered up or avoided in popular illustrations. His skin is bright red, because hell is conceived by modern Christians as an exclusively fiery place. This was not so with medieval Christians, as an examination of Dante's Inferno clearly demonstrates. He frequently has cloven hooves for feet, and when this is so his lower legs are often Satyr-like and hairy. Sometimes his teeth and fingernails are pointed. Sometimes his eyes are snakelike, having vertical slits in place of circular pupils. His tongue may also be long and serpent-like. He has a snakelike tail with a barb on its tip, and carried a pitchfork with either three or two barbed tines.
It is interesting to compare this recent version of Satan with his image in the 16th century, as shown in the French woodcut above. In the illustration, Satan sits upon a throne in hell. He wears a papal crown on his head. His face and ears are cat-like. Notice that his lower legs and feet resemble the talons of a hawk rather than the hind legs of a goat. His breasts are enlarged and feminine. In place of his penis is a hairy face with an open mouth. The tail that projects under his buttocks and trails over the seat of the throne to hang down between his legs is like the tail of a rat, and might easily be mistaken for his flaccid penis. Satan is attended in the illustration by a witch and a wizard, both of whom swing censors smoking with (undoubtedly) brimstone.
The wizard makes the sign of the Devil with his right hand as he reaches up to scratch Satan behind his feline ear -- this sign, with two fingers extended upward like horns, was illustrated by Eliphas Levi in his Transcendental Magic, Book I, Ch. 1 (it appeared in the French first edition of Book I of Levi's work, published in 1855 under the title Dogme de la Haute Magie). Levi labeled it "The Sign of Excommunication." I've reproduced it below for comparison with the hand gesture of the wizard in the old French woodcut, above.
If Satan is viewed as the Adversary, it made sense for Christians to depict him as the anti-Pope, the spiritual authority of hell. This portrayal of Satan was not a satire on the Catholic institution of the Pope, although after the Reformation Protestant publishers sometimes gave the Pope devilish attributes for purposes of political commentary.
Satan is best known in the Bible as the devil who tempted Jesus with power and glory over the kingdoms of the Earth, if only Jesus would worship him (see Luke 4:5-8). Here occurs the memorable line, "Get thee behind me, Satan." The Devil also set Jesus on a high pinnacle of the Temple at Jerusalem and dared Jesus to throw himself down to the flagstones below, to prove that he really was the Son of God (Luke 4:9-12).
The connotative difference between Lucifer and Satan is nobility. In spite of his fallen and defeated condition, Lucifer is always a noble figure. We must admire his courage and strength of will. Satan, on the other hand, is without redeeming qualities. He is wickedness for its own sake. In this sense, these two sides of the Devil are almost separate and distinct beings.
(Satanic sign of excommunication, from Eliphas Levi's Dodgme de la Haute Magie, 1855)