If you want to use Christian terms, I would say Satan corresponds with the Tempter, whereas Lucifer corresponds to the Paraclete. (see John 14:16-17 & 26, 2 Peter 1:19)
I see Satan and Lucifer as two terms for the same god. Which term I use depends on the context. Usually, I say Satan, but sometimes, I refer to the "Luciferian way of life", or the "Luciferian spirit".
I see Satan and Lucifer as two terms for the same god. Which term I use depends on the context. Usually, I say Satan, but sometimes, I refer to the "Luciferian way of life", or the "Luciferian spirit".