As one whom has studed Satanism and Luciferianism for the last couple years, I will answer your questions to the best of my ability.
Satanism and Luciferianism are often considered auxilaries of one another, some Luciferians and Satanists agree with this and don't mind beeing called either, others do care and wish for the to be seen as seperate{it depends on the individual Satanist/Luciferian, and in "some" cases a few orgs views}. Those against it are often some of the Luciferians, whom wish to seperate 'Lucifer" from "Satan"{since that the two were mixed together is a translation mistake made centuries ago with the Bible; and also because to some of them Lucifer is a more positive ideal/symbol}.
When one studied the many different sects and trains fo thought ecah of them has, one will find{in my opinion} that they are auxilaries; having some fundamental similarities and some fundamental differences as well{much like the two big brance sof Christianity, Protestantism and Catholicism do}.
The most notable differences are semantics; they both utilize both Lucifer and Satan as symbols, but the Luciferians place a greater emphasis on "Lucifer" and the traits associated semantically with this and with the myths-such as "enlightenment', "self-empowerment", "reason", and beieng a "light-bearer", Satanists place a greater emphasis on 'Satan" and the ideals semantically associated there{satan is the "adversary"}, however they both share many similar character traits, it's mainly semantics.
This and Luciferians do not bind themselves to Anton Laveys writings as much[but then again, there are a few Satanist sects that don't either].
Often Luciferians will be more open to spiritual ideas than Satanists whom more often are more focused on the carnal, but the Luciferian wil also be focused on the carnal{just not AS much so}; but then there are a few Satanist sects and trains of thought that are the same way as the Luciferians, such as the more Pantheistic "First Church of Satan" founded by former CoS{church of satan/laveyan} member John Allee{his focus is on "freethought satanism", because he saw the CoS and Laveys Satanism as abandoning it's roots for elitism,misanthropy,social darwinism,Ayn Rands Objectivism,midless selfishness/epicurean hedonism without proper balance, and a subtle authoritarian attitude} and the Deistic/Pandiestic Satanic Reds{ whom scientifically emphasis the "dark doctrines" which focuses on the "dark force" idea, Laveyans too talk about the "dark force"-but they tend to see it as a merely atheistic energy force and not rlaize that the roots of the "dark force' idea are indeed more deistic and more rooted in eastern philosophy such as the Vedas,Taoism/Daoism and others than in Western shock rock inversionism and christianity}
The FCoS, Satanic Reds, and many Luciferian orgs are more Daoist in their approach and using science,reason, and fcats they try to be a little more hednoistic in the sense of "universal hedonism"{which is a philosophy of wishing to see EVERY individual free to indulge themselves, which means also oposing many socio-poitical conditions that opress people; rather than merely ONLY looking out for number one period.}
Satanists and Luciferians both have Athiestic/Agnostics setcs and trains of thought and traditions, They both alos have more deistic ones, they both also have Pantheistic ones, polytheistic ones,and so on.
There is a common misconception that Satanists are all Laveyans and are mostly{if not completely] all Atheistic/Agnostic, and that Luciferians are those that worshop the devil and are theistic. But as I stated above this is not true. Both have different types.
As Satanism and Luciferianism are both HIGHLY individualistic, based on reason{sometimes mixed with faith, as in the case of strong atheists and theists}and personal experience, backed up by science and evidence as much as possible, it's pretty much impossible to pigeon hole them.
There's also a misconception that theistic Satanists/Luciferians worship the Christian devil{and there are smnall groups and a small minority of those out there that do this, they are for the most part rejected by ALL Satanists/Luciferians as "Christian Satanists" or "Reverse Christian devil worshippers"- even by most theistic satanists and Luciferians}, half truth at best.
Theistic Satanists/Luciferians tend to be either Pantheists or Polytheists, some might be duotheists or simple theists, but the Satan/Lucifer they worship and the devil they worship are/is more or less dissaciated from the Christian and Islamic ones{though for some, especially Polytheistic Satanists/Luciferians. the christian one may be one of the several or many in their own personal pantheon}, many Theistic Satanists/Lucifeirans and devil worshippers do not worship the christian one. Many theistic Satanists can be compared to beeing a form of "Dark Paganism" or "Dark Neo-Paganism"{"dark", not in the sens eof "evil' or "hateful" or "harmful",etc, but in a sense more like accepting that the Universe is not dualistic and neither are the gods or devils, they accept the positive and so-called negative or aspects of themselves in order to be more whole and self-aware and become more wise and mature human beeings; which is why all type sof Satanists/Luciferians take up the so-called "dark side", and "dark" often just means in the occult sense "hidden"}.
Indeed they are are very diverse, Luciferianism and Satanism. They have fundamental similarities and fundamental differences; which is why I often compare their differences or similarities as beeing like Catholicism and Protestantism in that way.
Also, some think the Luciferians to be more intellectual and cerebral, and Satanists more sense oriented; byt again, this depends on the individual and the scts or train of though/tradition.
both trace their infleunced WAY back, in some cases sharing some similar past infleunces, in other cases sharing different influences{philosophically,occulticly,historically, so on and so forth.}.
Both include variuos degrees of self-worship, some in a excessively arrogant and excessively hedonistic way, others in a lesser,more balanced way{including many Daostic type influences, amongst others} to moderate their own hedonism and ego[not deny such, just balance such}.
Here are links to Wikipedia on them both:
Satanism:
http://en.wikipedia.org/wiki/Satanism {which seems to focus mostly, if not only on the CoS/Lavey brand, whichis funny because up until recently it did'nt do this-it actually explained more diverse trains of thought; I suspect that the elitists in the CoS infiltrated it and altered it to their liking}
Luciferianism:
http://en.wikipedia.org/wiki/Luciferianism
[and it's various sects/traditions; also includes links to some different Luciferian groups; such as the "Church of Lucifer", "The Neo-gnostic Luciferian church of Denmark", "The Ordo-Luciferi{Luciferian order} and others]
Here are links from wikipedia{and direct links to orgs} on
a couple of the specific groups or types I mentioned:
"Dark Doctrines"/"Sat/Tan Satanism"/"Satanic Reds"=
http://en.wikipedia.org/wiki/Dark_Doctrines
http://en.wikipedia.org/wiki/Sat/Tan_Satanism
http://en.wikipedia.org/wiki/Satanic_Reds
http://en.wikipedia.org/wiki/Satanic_Reds
First Church of Satan{as founded by John Allee}=
http://en.wikipedia.org/wiki/First_Church_of_Satan
Ordo Luciferi=
http://www.ordo-luciferi.org/
for better understanding of theistic satanism:
http://en.wikipedia.org/wiki/Theistic_Satanism
{Diane Veras theistic satanism site}=
http://www.theisticsatanism.com/
Devil worship=
http://www.theisticsatanism.com/geifodd/
I include the links, so intgerested parties can do their own researhc if they truly wish to understand the two and their differences{wikipedia is a good source for this, as is googling and dooing research on the net.}
It's notable to mention that some groups that split from Laveys Church and type did so because they have a more balanced and compassionate and open-minded/free-though minset{as do 'some' Luciferian groups}- John Allee's FCoS is very much about tolerance and individuality; the Satanic Reds{the main expounders of the dark doctrines, are basically Socialistic/COMMUNE-istic Libertarians in a sense, and oppose exploitation of workers and people very much. They are "social realistists"}, misanthropy,social darwininism,elitism, and a odd sense of censorship have become the mark of Laveys CoS-and many Satanists and Luciferians dislike it for this very reason{it is turning into a cult of personaity and into an somewhat authoritarian group}
Some Shared influences or traits of the two;
first traits:
-Will.
-self-betterment,self-awareness/self-knowledge and self empowerment.
-ego gratification and hedonism{ot varrying degrees and in various contexts depending on the sect/tradition and individual}.
-seeing Satan or Lucifer as a righteous rebel much akin to other such divine rebels in human myhtology- such as the humanistic Prometheus.
-knowledge and wisdom.
Influences:
-Aleister Crowley and his Thelema{magickally or occultically}
-some other famous historical occultists{suhc as John Dee, Austin Osman Spare, and many others}
-the enlightenment and it's philosophies
-Roman and greek mythology and philosophy
-Sumerian/Babylonian/Egyptian mythology.
and others.
-Many also find alot of influence and inspiation from some Daoistic schools of thought and practice, some buddhistic, some Indian//Hindu/Vedas/sanscrit stuff. depending on the individual and tradition
As for yours truly,I've studied all traditiosn to variuos degrees, and experimeted with a few. I still experient with such to some degree{in a scientific manner, just to see if there be ANY validity to ANY occult ideas; Luciferian Satanism beeing my personal favorite inspiration in terms of "symbolic" religion}.
I've personally found much to gain in diffetent ways from a few different type sof Luciferianism and Satanism, and am interested myself in "Luciferian Satanism"{in an eclectic sense}, and have drawn "some' inspiration from the parts of Laveys own anti-theistic brand of Satanism[but I despise the social darwinistic,misanthropic,elitist,heirarchal, aspects of the CoS and Laveyanism, not to mention Laveys own made up personal legendary history-I hate liars}, I identify with 'some' of Laveys "Nine Satanic Statments though"{to varrying degrees} and "some" of his "11 Satanic Rules of Earth" and most of his "Satanic Sins"
http://en.wikipedia.org/wiki/Satanis...nic_Statements
Though some of them contain the ridiculous 'social darwinism","elitism",etc that I despise, and given the era in which Lavey wrote his Satanic Bible and founded HIS form/church of Satan{as if he had invented satanism itself, which he did'nt} he was a shock value reactionary{many deny this, but it is truth} and a bit of an inversionist.
I,however find more in common with more intellectual strains of Luciferianism{and some elements of openes to "spiritual ideas" depending on their level of scientific possibilities, I don't buy into some of the more absurd things}, plain occultism{elemets of Crowleys Thelema for one example}, and especially "dark doctrines" Satanism as explained in depth by the "Satanic Reds", their socio-political values to some degree, and their deistic take o the "dark force"{as explained in the following "9 Satanic Postulates":
http://www.geocities.com/satanicreds/9-sat-tan.html
in which SATAN is not derived from the hebrew but rather from two Vedantic words "SAT" and "TAN" menaing "pure existence/beeing" and "Unfolding from/becoming" respectively; and it has a very Daostic/Taoistic flavouring to it as well}. In this "Satan" is the deistic dark force; as many here know now I am a DEIST, I don't often call the Deistic first cause intelligence by anything that seems like a name-usually only by titles that describe it's function as the first cause creative intelligence, I sometimes call it "God" for conveniences/conventions sake, but "SAT/TAN-Satan" is as good a human word as any for it- as good as the human word "God". In a sense you could say I believe in the "Godevil{Goddevil/God-Devil}" or "Cosmocrator{cosmos creator/cosmos first cause intelligent creative force}. My idea of "god" fits well enough with those "satanic postulates"-hence I feel comfortable associating with them.
I like the Luciferianism, because of the emphasis of "light-bearing'{enlightenment}. and ebcause I equate Lucifer with Prometheus{ the divine fallen rebel/titan of myth whom stole fire representing progress,enlightenment,reason,etc, from the God Zeus whom I equate YhWh with, so humans could be free and enlightened rather than slaves to a God}.
Hence, I do not worship the cosmocrator{god/devil/firs cause} I just believe it exists as first cause and thatw e must live by the natura laws of it's creation and by the rationality/reason we as sentient creatures have developed.
Lucifer/Satan/Prometheus are good symbols of this.
The Baphomet{bitht eh Templars figure, and the modern goats head in a pentagram} and what it represents also symbolize these desirable traits and Cosmic Prinsiples of balance,nondualisn, and natural law.
Anyways, I hope this long essay on Satanism/Luciferianism sheds some "light" on the question fo what Satanism and Luciferianism are how they differ{or are similar}
Thanks for reading with an open-mind ladies and gentlemen.
In Reason:
Irrev.Bill