Ariel, a character in a play by William Shakespeare, necessarily exists in Poul Anderson's Shakespearean universe but does he also feature in Carolingian mythology? I assume not although someone might know better. In any case, when Ariel is also mentioned in Anderson's Carolingian universe, it is legitimate to ask: are there two Ariels, one native to each universe, or has a single Ariel originated in one universe and crossed over to the other?
This kind of question has arisen in other fictional multiverses. Thus, when Roy Thomas imagined that all Golden Age DC superheroes coexisted on Earth 2, he decreed that the Freedom Fighters, a superhero team, including Uncle Sam, who had fought the world-conquering Nazis of Earth X had not originated on Earth X but had crossed over from Earth 2.
In Poul Anderson's works, I concluded that there are two Kith Histories, one with a Star Empire, the other without. In James Blish's works, High Earth, the Traitor's Guild and the Green Exarchy are mentioned in a Dirac message but are also said to exist in a galaxy where there is no instantaneous communicator. Conclusion: two High Earth timelines. See here.