Is the Devil (Satan) different from Lucifer?

The word Lucifer is Heleel ben shachar, meaning son of the morning.

Rev 12:9 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.”

Rev 20:2 He laid hold of the dragon, that serpent of old, who is the Devil and Satan, and bound him for a thousand years”

So we see the one called the accuser, the one who lied to Eve is the Devil who is called Satan.
Luke 10:18 And He said to them, "I saw Satan fall like lightning from heaven.”

 Ezek.28:16 “By the abundance of your trading you became filled with violence within, and you sinned; therefore I cast you as a profane thing out of the mountain of God; and I will destroy you, O covering cherub, from the midst of the fiery stones”
 
He was quickly judged and lost his position in heaven in ministry to God.  V.17 “Your heart was lifted up because of your beauty; you corrupted your wisdom for the sake of your splendor.” pride came into his heart as he became enamored with his own beauty and wisdom.

Isa 14:12 "How you are fallen from heaven, O Lucifer (Day Star), son of the morning! How you are cut down to the ground, you who weakened the nations!

Yet Satan, who is formerly called Lucifer still has the ability to look as he once did, as a angel of light, of righteeousness.

2 Cor 11:14 “And no wonder! For Satan himself transforms himself into an angel of light.”(Lucifer =light bearer)

When he fell he became the accuser (God changed his name). He was the shining one covered by the precious stones, according to Ezekiel 28, stones that later appear on the high priests breastplate in the tabernacle of Moses’ time (Exodus 28:17-20), but their order is different.

Ezek.28:13 continues to tell us He was the choir director having a high priestly ministry. The leader of the angels  in heaven, the sons of God in worship, positioned above it as the canopy. (In Isa.14 we have insight into his attitude and actions that made him fall.) “
 
Lucifer is the Latin translation of the Hebrew word which means Day-star. Hebrew means “the shining one,” one who shines, describing his original state: This is why he can still appear as an angel of light. In his 5th I will: He says, I will make myself like the Most High. Satan tries to counterfeit God and his apostles (through men) when he appears as an angel of light or has a message that seems good to deceive people.