I've been reading up on some King Arthur literature the past few weeks and I've come across several pieces that mention the sword he pulled out from the stone to be Excalibur, and there are also some books that mention it to be named Caliburn
Are they one and the same or are they separate swords entirely?
No, not really. The Old French version of the name is Excalibur, while the same name in Latin is Caliburnus, shortened to Caliburn. The only difference is in what language you were talking about Arthur's sword. Like John/Jean/Juan/Johann/Ioannes are all the name 'John' in different languages.