To a Christian, Jew, or Moslem Lucifer is another word for the Devil or Satan. Few however are aware that lucifer is never mentioned in the bible, not as 'lucifer' per se, not once. Satan is mentioned multiple times. The books of Chronicles, Job, Zechariah. Matthew, Mark and Luke all give that Devil his due. In the Quaran / Koran - ditto - multiple mentions of Satan, but no lucifer.
Lucifer is a name / title that derives from the planet Venus which appears as the morning star both in our present reality and scriptural history. Lucifer, as a name for the Devil can be traced to Isaiah 14:12. The English translation took the Latin word 'light-bringer', which was used for venus, the morning star and translated it as lucifer.
[Isaiah 14:12. How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations! ]
The Old Testament narrative, as preached by Isaiah ties into the Fallen Angel legends which are not extensively covered in the canonical literature. Bypassing all the scholarly speed bumps and theological mumbo jumbo lucifer is basically representaive as the leader of the Fallen Angels who was tossed from heaven to reign in Hell.
In Miltons 'Paradise Lost' He is a tragic entity, once the most beautiful of all angels. Lucifer infamously declares: "Better to reign in Hell than serve in Heaven." Following a failed rebellion against God / Jehovah, he is cast out of Heaven and condemned to Hell.
After being cast from Heaven Lucifer is replaced by the Archangel Michael as the morning star. He is no longer the 'light bringer' or 'lucifer' he is now referred to as Satan. So yes, so far as Judeo-Christian lore is concerned Lucifer and Satan are one and the same.
Lucifer outside of Judeo Christian lore however predates these Abrahamic faiths, He is a pre Christian deity of ancient Roman and Greek mythology. He is mentioned in 'Metamorphoses', circa 8 B.C and the, Roman poet Virgil mentions him as far back as 29 B.C Plato mentions him in 360 B.C.
References to Lucifer in antiquity sometimes refer to more of a title than a deity or personage and translations of "Light Bearer" or "illuminator" are sometimmes skewered in their meaning and relationship to the modern day incantation of Lucifer and luciferianism. Modern day luciferianism is Service to ones self, disregard of community, exploitation of others. Greed is good, or in the words of Aleister Crowley 'Do what thou wilt shall be the whole of the Law'