Lucifer = Satan?

[TonyChanYT]

Isaiah 14:

4 you will take up this taunt against the king of Babylon: How the oppressor has come to an end! How his fury has ended!
12 How you have fallen from heaven, morning star, son of the dawn! You have been cast down to the earth, you who once laid low the nations!

O Morning Star,
הֵילֵ֣ל (hê·lêl)
Noun - masculine singular
Strong's 1966: The morning-star

The morning star refers to the king of Babylon. Some interpret it as a metaphor for Satan.

King James Bible:

How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations!

Merriam-Webster:

Lucifer has been in the English language for a very long time, and has not solely carried the meaning of "Satan." The word comes from a Latin root—lucifer, in Latin, means "light-bearing"—and has also been used by poets to refer to Venus, the morning star.

Lucifer = Satan?

Very loosely speaking yes. Strictly and scholarly speaking, no. The word is not even Hebrew. It is Latin. I prefer to stick to the wording of the Scripture. "Lucifer" is not Scriptural. The Hebrew word for Satan (H7854) does not even appear anywhere in the books of Isaiah.

Also, see the role of satan.