There are two different stories of how King Arthur received his sword, Excalibur. The first is that he pulled it out of an anvil or stone slab (and by doing so confirmed that he was the rightful king of the land). The second is that he received it from the Lady of the Lake (and that he had to return it to her before he died).
Which one of these stories is correct? Or did King Arthur have two different swords that he got different ways?
The Excalibur problem is that, over time, people have combined two different Arthurian swords into a single blade. This is a serious pet-peeve of mine.
Most popular depictions (especially in recent years) tend just to use one sword or the other and call it Excalibur. However, some find a way of placing the sword in the position of both: e.g. the Lady of the Lake puts it into the stone, or something to that effect.
Older texts, however, do make the distinction clear even if it's a "blink and you miss it" moment. For example, a sentence saying that the sword in the stone was fragile, and couldn't be used for combat, so Arthur went to the Lady of the Lake for a new one.
In the medieval "Alliterative Morte d'Arthur" the roles of Arthur having the two swords is actually really important: Part of Mordred's coup involves stealing Clarent (establishing that he has the mortal right to rule by laws of men) in addition to kidnapping/"marrying" the queen. The final battle involves Arthur, wielding Excalibur (divine right to rule), versus Mordred, wielding Clarent. The two then destroy each other.
I really hope this helped clear things up for you. I'd recommend starting with Geoffrey of Monmouth and working your way through medieval texts to see the evolution of the depiction of Arthur's swords.
The short version is that both of those swords are Excalibur. Le Morte D'Artur is, to be blunt, incredibly self-contradictory in places. Malory took a number of existing stories and collected them without always concerning himself with conflicts between them.
In Robert de Boron's Merlin, Arthur obtained the throne by pulling a sword from a stone. In this account, the act could not be performed except by "the true king," meaning the divinely appointed king or true heir of Uther Pendragon. This sword is thought by many to be the famous Excalibur, and its identity is made explicit in the later so-called Vulgate Merlin Continuation, part of the Lancelot-Grail cycle. However, in what is sometimes called the Post-Vulgate Merlin, Excalibur was given to Arthur by the Lady of the Lake sometime after he began to reign. She calls the sword "Excalibur, that is as to say as Cut-steel." In the Vulgate Mort Artu, Arthur orders Griflet to throw the sword into the enchanted lake.
Caliburn was the sword in the stone, but was broken by Clarent during the battle between Arthur and his illegitimate son Mordred. Excalibur was given to Arthur by the Lady of the Lake in order to defeat Mordred, and it became Arthur's second sword while Caliburn was said to not only declare the one true king of England but was supposedly unbeatable as long as the wielder's heart was pure.
Arthur's heart grew dark from his hatred towards his step-sister, Morgan le Fay, and that's why the sword broke. Excalibur was made to be the opposite to Clarent, therefore becoming the sword of ice while Clarent was the sword of fire.
These are the major differences between the three swords
