After doing some Google searches, it looks like it is two different words in the original text.
Should the Bible say Lucifer or morning star in Isaiah 14:12? And does it refer to Satan?
Throughout the world, if you ask people who “Heyleel” (hey-LEYL) is, most will not know what to answer. But if you ask them, “Who is Lucifer?” you will very likely get the correct answer. People know who Lucifer is. Ask the Luciferians, who worship Lucifer as a being of light. Ask the Satanists, who call their master Lucifer. No one is in doubt as to who Lucifer is.
What if you ask them, “Who is the morning star?” or “Who is the day star?” Most will know it’s Jesus. Look at these scriptures:
2 Peter 1:19: “We have also a more sure word of prophecy; whereunto ye do well that ye take heed, as unto a light that shineth in a dark place, until the day dawn, and the day star arise in your hearts:” Revelation 22:16: “I Jesus have sent mine angel to testify unto you these things in the churches. I am the root and the offspring of David, and the bright and morning star.”
Any translation that says “day star” or “morning star” or “star of the morning” in Isaiah 14:12, like most modern perversions, is bringing confusion. And God is not the author of confusion (1 Corinthians 14:33). Many people reading the modern perversions end up asking, “If Lucifer is the morning star and Jesus is the morning star, then is Lucifer Jesus?” The modern translations are simply not clear!
That is not all. The term translated "Lucifer" does NOT at all mean "morning star" or "star of the morning." That would be two totally different Hebrew words. The word means "light-bearer." In Greek it's "heosphoros," “light-bearer.” In Latin it's translated "Lucifer," light-bearer. Whether you say "heylel," "heosphoros" or "lucifer," the meaning is the same: "light-bearer." But only Lucifer communicates who we are talking about in English.
And not only English uses the term. Look at these ancient translations of the word. They also use some form of “Lucifer.”