Why Conflated? It is with the presumption that Isaiah's vocabulary (Lucifer, trans. Jerome) is a reference to Satan that Ezekiel's passage is therefore also assumed to be a reference to Satan because of the exalted, figurative language used by Ezekiel. People are led astray by the lofty language used, and rush to jumble them together.
People who are haven't studied the type of literature of the ancient cultures of Egypt, Babylon, Persia, Assyria, et al. are easily led astray by this verbage in Ezekiel. But scholarly research in Archaeology, Anthropology, Ancient empires, etc. reveals that Kings and Pharaohs were described in all sorts of references to divinity, and heavenly aspects! E.g. the Pharaohs were descendants of the gods, Ra, Thot, etc. Later the Caesars were "Augustus" and considered divine. Monuments, murals, and inscriptions depict all of this.
It is the King of Tyre who is specifically addressed in Ezekiel (and next, Sidon) who was head of the Phoenician mercantile empire. He was being called out because of deceitful trading (verses 5, 16, 18), and putting his confidence in his extravagant wealth.
To introduce the concept of Satan here is highly unwarranted. TheIt wasn't Satan who was being called out because of his "deceitful trading"! So the figurative illustrations and verbage is just common grammar of the ancient people...perhaps used in a mocking way.
To advocate Ezekiel's passage as a reference to Satan (Lucifer) would require more substantial hermeneutical proof. It just isn't there. Tradition---and pulpit rumors---have a way of distorting the original texts. Background resource materials (history, archaeology, geography, etc.) are vital for coming to a clear understanding of any scripture.
Further Research For more details on this topic see Question BH 22364, Is Satan the master of music?.