My own opinion (and only my opinion, I'm no expert yet) is that, from my reading of the texts that mention those labels or names, they are not the same. Lucifer is the fallen angel, the light bringer, led the rebellion against god and was cast out... the one most xtians now refer to as Satan. However, their own bible uses the term Satan in a different context, as it simply translates as the Adversary. In the book of Job, god asks "a satan" to tempt Job as a test, and they almost chat like co-workers about it. This "satan" seems to be more like a prosecutor who works for god. I believe this might be the same "satan" Jesus refers to in the wilderness, as it also tempts him, possibly as a test set by god. However, having said all that, just because the word Satan is used in different ways in the xtian bible, doesn't mean that what it has evolved to mean isn't also true. To me, Satan is a title, and when I devoted myself to Satan I devoted myself to the being or beings who fit the title of adversary to the xtian god, to jesus, to all that is holy. I believe that Lucifer is one of those beings, if not the only being who I currently worship as Satan. These are just my own thoughts, and I'm still learning more and more every day with the help of all my Satanic Brothers. Hail Satan!