I have nothing to add to your and Aurora's explanation
Some words perhaps about ffwitchy - which is, the Witchking as he is shown in Fanfiction.
Some game came up with the idea of extending the history of the Nazgūl as it might have been, give them names in Tolkien's languages and so on. This means that this information *might* perhaps be true, nothing is different than Tolkien tells us, it's just more information. Some say adding something to Tolkien's work is nonsense, some say why not it's interesting. Your problem to decide what you think.
Well, according to this fanfiction-stuff, Murezōrs name was Er-Mūrazōr which is translated "the Black Prince" - compare Ar-=King.
He is said to be the brother of King Tar-Atanamir the Great of Nśmenor, so he was the second son of Tar-Ciryatan the Ship-Builder. He was born in Second Age 1820 during a solar eclipse with raven-black hair, so he was called "Tindomul" which means "Son of Twilight". He was fiery and aggressive and always supported the Nśmenórean interests. On a rapid conquest in Middle-earth, he reached Barad-dūr, the Fortress of Sauron, in the first week of S. A. 1883 where he became a pupil of the Dark Lord and expanded his knowledge of spells and wizardry during the following 115 years, until Sauron offered him a Ring of Power in 1998 and promised him wealth and immortal power.
Some time in the Third Age, Sauron sent him to the North in order to found a stronghold in Northern Arnor which later became known under the name "Witch-realm of Angmar" (therefore he was called the Witchking, being a master of Witchcraft). During long years, he was in war against the armies of Arnor but eventually conquered Cardolan and Rhudaur - if conquer is the right word here, well, the lands fell under his dominion, but Earnur's allies of Arthedain vanquished the hosts of Arnor near the capital of Arnor, Annśminas the Western Tower.
In this time Glorfindel prophecied that the Witch-king would not be killed by any man.
Later at the end of the Third Age, the Witch-king led the army fighting at Osgiliath and then rode to the Shire with the other Nazgūl in order to find the One Ring.
He stabbed Frodo with the Morgul-knife on Weathertop; at the Ford of Bruinen, he and the other Ringwraiths were engulfed of the enchanted river. After that disaster, he returned to Minas Morgul and later led the hosts of Sauron against Minas Tirith. There he fought against Gandalf and the Rohirrim; when Théoden was killed under his horse, his niece Eowyn challenged Witchy with the words "But no living man am I! You look upon a woman. Eowyn I am, Eomund“s daughter. You stand between me and my Lord and kin. Begone, if you be not deathless! For living or dark undead, I will smite you, if you touch him". He broke Eowyns hand holding her green shield, but Merry plunged his sword into the knee of the Lord of the Nazgūl and so Eowyn could kill him.