I agree that it s both - the king because Scrioture says so AND Satan due to the symbolismI agree.
But in the Hebrew, which is what most of the "Old Testament" was written in, it is "helel" (הֵילֵל ) ...
Which has several meanings;
In the Latin, it is rendered as "Lucifer".
It means "lightbringer", or "son of the morning"...which is what the Lord created him to be.
In any case, the one who fell from Heaven, the one who ( in his arrogance ) claimed to want to be like the most High, was "Satan" ( which means "adversary" ).
..and whoever is being spoken of in Isaiah 14 here:
" 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!
13 For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation, in the sides of the north:
14 I will ascend above the heights of the clouds; I will be like the most High."
To me is indeed the very same person who led a revolt in Heaven and took 1/3rd of the angels with him when he was cast out.
The reference of "Lucifer", right or wrong, is who I know to be Satan.
Regardless, it seems that we disagree... and it seems that we will have to stop there.
My point is that הֵילֵל is not Satan's name just as "bright and morning star" is not Jesus' name.