I see both as figures that derived from mythology.
Satan was probably based on Set the counter-god of the ancient Egyptians, the brother of Osiris who killed him and became the god of the untamed desert and the underworld. Set is Apep who dwells in Amenti (the underworld) and tries to stop Horus' sun-ark each morn before it rises to the world above. Thus Set/Satan is Choronzon the devil who tempts adapts who journey through the Abyss and seek to be reborn as Masters of the Temple. Koronzon was the name given by Satan to John Dee and Edward Kelley in the 16th century. He is the snake coiled around Da'ath (Knowledge) the hidden Sephira on the Tree of Life, the guardian of occult wisdom and knowledge.
Lucifer was based on a misreading of Jerome's Latin Vulgate in which "day star" in Isaiah 14:12 was translated as Luxiferre, a Roman name for the "morning star" or the planet Venus when it appeared at morn before the sun came up. Luxiferre, anglicized to Lucifer, means "light-bearer." Lucifer got mixed up with Prometheus who gave mankind fire from the gods and made men like the gods themselves. Zeus told Prometheus not to give mankind fire because then they would become powerful like the gods. The discovery of fire is what lead mankind out of the cave-dweller lifestyle and brought about the evolution from Neanderthal to Modern Homosapien. Thus Lucifer is the snake on the Tree of Knowledge that gives carnal man the knowledge to become god and control his own destiny. Lucifer is also fallen Sophia, the Gnostic goddess who fell into Chaos below the Pleroma and gave birth to the demiurge Yaldabaoth. After Yaldabaoth (Yahweh) made the first man and woman Sophia appeared as a snake on the Tree of Gnosis that mysteriously appeared in the garden. Sophia gave Adam and Eve the knowledge to transcend matter to the realm above and become like god. Sophia the fallen goddess is Venus (goddess of love) who rises every morn before dawn and leads mankind out of darkness to the realm above, Lucifer the "light-bearer." The Gnostic Mandaeans who exist to this day pray to the stars as divine beings. A symbol common to both Satanist/Luciferians and Gnostics is the Pentagram. To Satanists/Luciferians the Pentagram is Baphomet, with the horns on the two upper points and the letters LVTHN (another name for the demiurge or serpent of Chaos) at each point. The Gnostic Cathars revered the Pentagram. The Pentagram is also sign of Venus the "morning star" who appears in the east just before dawn and coincidentally the symbol of the Eastern Star in Freemasonry.
I see both figures as existing metaphorically, but representing real concepts. Both bring transcendence from authoritarian/patriarchal religion. They are the serpent or snake in Tantra that climbs up the tree (spinal column) to awake Shiva in the brain.
Thelema 101 at Thelema 101 Sinagogue of Satan The Gnosis Archive: Resources on Gnosticism and Gnostic Tradition Jungian archetypes - Wikipedia