I know this is an older question, but since there was no selected answer, I thought I'd give it a go. The answer is going to depend a lot on the denomination that is answering, so I will approach this from a purely non-biased, non-denominated, purely Scriptural point of view.
Now, are Lucifer and Satan the same being? Yes and no.
As an adjective, the Latin word lucifer means "light-bringing" and was applied to the moon. As a noun, it meant "morning star", or in poetry, "day". This word, being Latin, actually should not exist in English translations, and should actually be translated into one of the above options. This word is a Latin translation of הֵילֵל, read as hêlêl or heylel.
Isaiah 14:12 is not the only place where the Vulgate uses the word "lucifer". It uses the same word four more times, in contexts where it clearly has no reference to a fallen angel: 2 Peter 1:19 (meaning "morning star"), Job 11:17 ("the light of the morning"), Job 38:32 ("the signs of the zodiac") and Psalms 110:3 ("the dawn"). To speak of the "morning star", lucifer is not the only expression that the Vulgate uses: three times it uses stella matutina: Sirach 50:6 (referring to the actual morning star), and Revelation 2:28 (though this might actually use the word "lucifer" or "lux ferre") and 22:16 (referring to Jesus).
Another fun little note is that the Exsultet includes "lucifer" in clear description of Jesus Christ. Use of "Lucifer" as a names popularized by Dante Alighieri's Inferno and John Milton's Paradise Lost.
In regards to Isaiah 14:12, translating the actual line gives us "Hillel ben-Shahar", which very well could have been the name of Babylon's King, being that Hebrew contains no indications for capitalization.
Now for Satan:
Satan comes from the Hebrew word שָּׂטָן (pronounced "satan"), meaning "adversary", "accuser", or "enemy". The original Hebrew term is a noun/verb meaning “obstruct, oppose,”. It is almost always accompanied by the prefix "ha-" in Hebrew, meaning "the" in English - thus "the adversary", "the accuser", etc.
So back to the question, are Lucifer and Satan the different beings?
Yes and no.
Lucifer, whether Isaiah was writing about the Devil or not, was clearly an enemy of God and His people - so he would have been "ha-Satan", the enemy. If Lucifer is in fact the Devil, he is both the enemy by the Hebrew definition and Satan as we know him.