This is something that comes up every now and again and it's an excellent question.
LDS scholar Ben McGuire explains:
I am going to start off by saying that most of what appears on the Web link which you forwarded is nonsense. They give largely erroneous responses. While the Hebrew text is accurately noted, the quality of information goes downhill from there. Let me point out the major error, and then we can discuss the real meaning of the passage in Isaiah.
Jerome translates it as Lucifer in his Latin text–this, your article claims is the starting point for the connection between Lucifer and Satan.
Actually, Lucifer is first mentioned (under that name) in the writings of Origen (end of the second century) some two hundred years before Jerome puts it into his Latin text. Tertullian and others of the early fathers of the church also discuss Lucifer, so the connection between Lucifer and Satan was established some time prior to the end of the second century. Before the Latin text becomes widespread, however, the name Lucifer had a much more specific meaning. It was the name of Satan prior to his fall from glory. Origen explains that this is because prior to his fall, he was a being of light and thus it was an appropriate description of him. After his fall, Origen continues, he was no longer a being of light and became known as Satan.
The second point is that the scholarly community almost universally rejects the being identified as helel ben shahar in Isaiah 14 as being the king of Babylon directly. There is a figure in contemporary Canaanite religion which resembles Helel in Isaiah 14. That figure is ‘Athtar. At one point in Canaanite myth, ‘Athtar attempts to sit in the throne of Ba’al, the king of the gods. He fails in his attempt, and instead descends to the earth to rule there. ‘Athtar is known in southern Arabian inscriptions as Venus, or the Day Star. More than this though, is the account in Isaiah. The “stars of God” is a reference to the divine assembly–all of the divinities of heaven. The mount of the congregation in the sides of the north (in the original Hebrew) is equivalent to Canaanite phrases describing the dwelling place of Ba’al. So, in effect, we have in Isaiah a description of a divinity who wants to seize the throne of Ba’al and rule the heavens. Of course there are differences as well as similarities, but I find this argument to be fairly convincing myself.
While the Web-site article you reference tends to look at the literal meaning of the words, instead of examining them as names, it completely loses the rest of the context of the narrative. There is no basis in Isaiah’s charges as they would apply to the Babylonian king. It is primarily on the similarities between the Isaiah text, and text covering the Ba’al/’Athtar myth that this connection is drawn. (For bibliographic references and a description of the related scholarly arguments I recommend this article (the most recent on the subject that I am aware of): “The Mythological Provenance of Isa. XIV 12-15: A Reconsideration of the Ugaritic Material” by Michael S. Heiser, in Vetus Testamentum, 51/3 [2001], p. 354-369).
At the same time, this concept is, interestingly enough, seen in the New Testament. Jesus claims that he saw Satan “fall like lightning from heaven” and in John and Paul we find Satan described as the “God of this world.” It was these references (among others) that led the early fathers of the Christian church to conclude that Helel in Isaiah 14 was Lucifer and also Satan. The similarities between their beliefs, and what they saw in the Old Testament texts came together to form a lasting opinion. And when the Latin text named the being in Isaiah 14 as Lucifer, that tradition has been followed ever since.