My mother was born in the Sub-Carpathian region of what was then Czechoslovakia, but in her parent's time, it was part of the Austro-Hungarian Empire.
As such she grew up utilising many variations of her name (as did many others of this region).
She was born with the given Yiddish name of Scheindel, which means beautiful....and so her Hebrew name was Yafa (meaning 'beautiful' in Hebrew).
To her Hungarian friends and when speaking Hungarian, she was known as Sari/Shari.
On her Czech documents and at Czech School, she was Charlotta and whilst attending Russian School, she was Zlate or Slava.
In English, she was Charlotte.
Other variations of usage I've noted are Jennie (Zseni) in English.
The name Sari, is more typical of Hungarian background and hence, used in those parts that were once a part of the Austro-Hungarian Empire eg. Hungary; parts of former Czechoslovakia (Slovakia & Sub-Carpathia) and parts of Romania. Its possible that Sara could be interchanged, however it's not usual practice and is more likely a different name.
Sara/Sarah in Hebrew, would be more commonly used the same in Yiddish as well as usage of Szure; Surele/Sarale; Sore etc. and likely Suri/Szuri or Szerin in Hungarian. In English, some of the usage would be again Sara/Sarah; Serena or even Shirley and Sadie.
Hope this helps.