The Infernal Concept: A Short History of the Devil's Kind
The Great Work is a lifetime dedicated to reaching one's Holy Guardian Angel and thus perfecting one's soul on the alchemical path - the alchemy of spirit and the alchemy of matter. This is largely a Western Mystery Tradition concept seen in the works of the old hats like Eliphas Levi, Israel Regardie and Aleister Crowley.
Satan as Symbol and the People's Voice
Satanism, as defined by Anton Szandor LaVey, is not about the Great Work. It is not even about spiritual integration nor enlightenment, what he refers to as 'spiritual pipe dreams.' Satanism is defined profoundly and perfectly in the Nine Satanic Statements as written in the Satanic Bible:
Magic is used in very specific contexts - Compassion, Lust, and Destruction. No magic of higher spiritual awareness, nor reaching one's Holy Guardian Angel. Those that wear the Devil's Mark are not bound by any spiritual dogma nor condemned by any religious proclamation. We are here to indulge, to experience, and to hold our Selves in the highest regard before anyone or anything else.
This differs from The Satanic Temple, of which I am a Card Carrying Member, in that they take Satan as the symbol of rebellion and art. Rebellion against the State and it's often abusive and bigoted laws. They fight against tyranny in all its forms. Like Lucifer raised his sword to God and the army of Michael, the Satanist raises their voices and banners to the fascism of modern politics.
Both are valid paths to Satan, although they are largely atheist in approach. Now we move onto Demonolatry, a path of Theistic Satanism.
Demonolatry and Devil Worship
Demonolatry may have been practiced in secret for centuries, but that is pure speculation. What is a fact is S. Connolly wrote the defining book for Demonolaters, The Complete Book of Demonolatry. Honestly, I have not read it but I have read all her free PDF's and was part of an international forum on Facebook several years ago. They believe demons are quite real, they are the definition of Devil Worshippers. Honestly, it's nice to see Satanists not shake like wet dogs when it comes to the question of whether they worship the Devil or not. Satanism, as branded by LaVey and Greaves, is almost made for the mainstream. Demonolatry (and Luciferianism... we'll get there in a moment) are far less mainstream in concept and design.
Demonolatry is similar to Wicca where you seek your Matron or Patron Demon (or Devil). They often come from the Ars Goetia, but just about any dark deity will do. Hekate was my Matron for years, but my path has expanded and I have now since found myself in the 'dark night of the soul' (to take the phrase from St. John of the Cross) where I am Matronless and Patronless as I am redefining what it means to be a Sorcerer.
Demonolatry differs from Wicca on many levels, though. Many practitioners prefer to offer their own blood in ritual and have no problem with cursing people. It is a very individualistic path, as ones aesthetic and ritual design can often be influenced by one's Matron or Patron.
The other unique practice Demonolters use are called Enns, which are syllabic chants similar to Sanskrit Mantras. They are single sentences chanted repeatedly until one enters an altered state where communication with one's Matron or Patron can be achieved.
One of the defining people for Theistic Satanism was Diane Vera. I believe her website is still around, but you may have to do some digging. It's where I learned about Theistic Satanism in the first place. I really enjoyed her website as it was a mature perspective and not filled with the silliness of edgy teenage drama.
Luciferianism and the Draconion Orders
Finally, we come to Luciferianism. Two Orders of which I have been fond of are the Temple of Ascending Flame and The Order of Phosphoros. Temple of Ascending Flame was founded by Asenath Mason after her split with the Dragon Rouge, a highly respected Draconion Order in Sweden (founded and headed by Thomas Karlsson). The Dragon Rouge helped define the Qliphoth and its ritual methods. There isn't much known about Dragon Rouge outside of their website and books by Karlsson (which I highly suggest you seek out! They are works of art and dark wisdom!).
Temple of Ascending Flame is a free online Magical Order, but don't think that makes it easy! You are expected to offer your blood for most of their rituals. The probationary period is 6 weeks of daily rituals of which you write a report and send to the Order. I never got past the probationary period as I no longer agree with blood magic unless it is from someone with a menstrual cycle that utilizes it. No reason to self harm for magic! Qigong is a non-bloodletting form of blood magic. Someday I may write an article specific to this.
Finally, we have Luciferianism as defined by Michael W Ford, founder and High Magus of the Order of Phosphoros. He has a few offshoots, including the Assembly of Lightbearers, which acts as a Church for Lucifer. Luciferians follow the 11 Luciferian Points of Power:
Ford considers Will, Desire, and Belief the three tenets of magical ritual. Without Will it is merely wishful thinking, without Desire your intention falls short and without Belief you are empty of conviction (for the ritual). He also talks about Deific Masks, the many faces of the deities the Luciferian works with. Each Deific Mask serves a purpose towards ritual and apotheosis. Ford works with several paradigms of 'Witch Blood', including Yatuk Dinoih (Avestian Witchcraft), Kessipim (Cannanite Witchcraft), Akhkahru (Vampiric Witchcraft), etc.
Conclusion
There is no single philosophy nor doctrine for Satanism. The main guidelines are individuality, dark symbolism, and counter culture (The Church of Satan call themselves the 'Alien Elite'). Most paths practice a form of magic and all practice a form of ritual, but their concepts of what ritual is differs.
The Satanic Bible defines ritual as a form of Psychodrama, The Satanic Temple defines ritual as a form of protest, Demonolaters see ritual as a form of devotion and spell work and Luciferians understand it as a path to Apoptheosis. All forms see it as a form of psychological manipulation of the Self. It is a form similar to Jungian Shadow Work in certain contexts, on how to face ones subconscious and learn to work with ones 'inner demons' rather then try to avoid or destroy them. Satanic magic is mainly about self empowerment and this 'magic' can be done in the Ritual Chamber or by ones aesthetic.
Satanism isn't for everybody, nor should it be. For some it is merely a phase, and that is well and good, but for me it has been a defining path of rebellion and antinomian magic since I was a teenager. I hope you have found some use in this post and continue your own research and advancement of the Infernal Concept.