According to both Grant and Crowley, Set/Satan/Lucifer/Horus/Hadit/Hoor-Paar-Kraat/Ra-Hoor-Khuit are all in fact the same Devil on some level.
"Shaitan, Satan, or Set, is Hoor-paar-Kraat, the concealed aspect of Horus,whose manifest side is Ra-Hoor-Khuit. Shaitan is the God of the South, yet his votaries face North when invoking him. Dion Fortune observes that "Crowley gives the North as the holy point towards which the operator turns to invoke, instead of the East, whence light arises, as is the classical practice. Now the north is called ‘the place of the greatest symbolic darkness’, and is only the holy point of one sect, the Yezidees, or devil worshippers."
The Magical Revival by Kenneth Grant
“AIWAZ, the solar-phallic-hermetic ‘Lucifer,’ is His own Holy Guardian Angel, and ‘The Devil’ SATAN or HADIT, the Supreme Soul behind RA-HOOR-KHUIT the Sun, the Lord of our particular unit of the Starry Universe.” - Crowley
“Horus is a twin, two in one. Horus and Harpocrates are one, and they are also one with Set or Apophis.” - Crowley
“The Book of the Law—the New Gnosis, the latest Tantra, the most complex Grimoire—from a praeter-human Intelligence named Aiwaz, a messenger of that most ancient god whose image was worshipped in the deserts under the name of Shaitan, and, long ages earlier, as Set, the soul or double of Horus.” - Grant
““In The Book of the Law, Hadit (or Set) declares ‘I am eight, and one in eight.’” - Grant