Queen Elsa of Arendelle and Elphaba Thropp from Oz have never met in canon, as they are from different worlds.
Nevertheless, the two characters share some striking similarities. Both of them originate from a re-imagining of villains from two well-known children's stories (Hans Christian Andersen's titular Snow Queen and the Wicked Witch of the West from L. Frank Baum's The Wonderful Wizard of Oz) as anti-hero protagonists. Both characters are magic wielders, and both are largely isolated because of a feature that they were born with: Elsa's ice powers and Elphaba's green skin. Elsa is later branded a "monster" by the Duke of Weselton, while Elphaba is denounced as a "Wicked Witch" by Madame Morrible.
Elsa's story centers around her relationship with her sister Anna, whom she initially feels she has to keep at a distance to protect her from her ice magic. When her powers are publicly exposed at her coronation, Elsa flees, leaving Anna to look after the kingdom in her stead. Elphaba's story focusses largely on her close relationship with her roommate-frenemy-turned-friend Galinda, with whom she amicably parts ways when she flies away.
Both characters' stories are told through the medium of a musical, with Elphaba and Elsa both having been portrayed by Idina Menzel. Elsa's song "Let it Go" and Elphaba's song "Defying Gravity", both sung by Menzel, are immensely popular anthems to personal freedom, representing a pivotal point in the respective characters' narrative arcs, where they decide to fully embrace an aspect of who they are that they have previously repressed, defying authority and the expectations of the other characters in the process. Elsa decides to abandon Arendelle and flee into the mountains where she can fully embrace her ice powers without (as far as she knows) hurting anyone, while Elphaba, having become fully disillusioned by the Wizard and his treatment of animals, decides to go along with the appearance of being the "Wicked Witch" that she has been slandered with, flying away on a broomstick.
The similarities between the two characters have made this a fairly popular crossover pairing, either as a romantic ship, or a platonic friendship, or a composite of the two characters. While in Wicked AUs, Elsa is commonly cast as Elphaba and have Elsaba as Elsa's nickname whenever fans draw her as a self version of Elphaba, by turn Elsa's skin green and her hair and signer dress black.
|SHIPS||het||Agduna • Hanna • Helsa • Hiccanna • Hiccelsa • Janna • Jelsa • Kristanna • Kristelsa|
|femslash||Elsaba • Elsamaren • Heathelsa|
|poly||Hansoffanna • Kristelsanna|
|friends||Annolaf • Krisven|
|CHARACTERS||m/f||Anna • Elsa • Hans • Kristoff Bjorgman|