Both characters are often confused in modern day parlance and sometimes used in place of the other.
In Christian mythologies, Lucifer is regarded as a beautiful and powerful angel before he fell to sin. in the Book of Isaiah for instance, the interpretations often referenced Lucifer as a morning star. So, from that aspect, Lucifer is seen as the heavenly beautiful morning star who fell from grace. After falling from grace and out of the light of God, he became the opposite of what God represents. Because Lucifer was no longer in the light of God as an angel of the most High, he became Satan – a direct opposite of God.
In the Bible and Quran for instance, Satan is seen as an accuser or used to term all devils. In the Book of Job, Satan is seen strolling in to do his duty, accusing God of making it all easy for Job. Again, the reference to Satan as an accuser can also be traced to the Book of Revelation when the great accuser was cast off from heaven. From the analogy above, it can be said that while Lucifer was the heavenly angel, he became Satan after he fell to sin, making them both the same persons but different personalities altogether. But, that’s for Biblical interpretations and mythologies.
In Igbo tradition and culture, the being “Ekwensu” is often misinterpreted to be Satan. Ekwensu is a a God of war and trickster God in Igbo traditional myths and legends. In some myths and legends, anyone who call on Ekwensu before embarking on any war never loses the battle.
Coming back to Lucifer again. Lucifer is used in reference to the movement of the planet Venus in its orbits. The disappearance and reappearance of the planet in its movement round the sun got it the name ‘Lucifer’ or “morning star” in ancient times. In Babylonian mythologies, the movements associated with Venus is referenced in the myths of the Babylonian God – Ethana.
According to the Jewish Encyclopedia –
“The brilliancy of the morning star, which eclipses all other stars, but is not seen during the night, may easily have given rise to a myth such as was told of Ethana and Zu: he was led by his pride to strive for the highest seat among the star-gods on the northern mountain of the gods … but was hurled down by the supreme ruler of the Babylonian Olympus.”
Lucifer Morningstar of DC Comics.