I had the same question and did a little digging. So here's a bit of history on this piece and some background on its composer, Grigoras Dinicu.
It seems Heifetz adapted the original violin piece as a duet with piano, from the original violin solo. The violin solo itself did not seem to have changed, but Heifetz at the time was looking for small pieces he could use for his encores, with a piano accompaniment, and this was one of the pieces he collected, and adapted for the violin and piano for himself and Emmanuel Bay.
The original version is no longer available because Dinicu signed his rights over to Heifetz. Dinicu wrote it as a requirement for his conservatory studies, and as such it was already properly written and recorded by the time Heifetz heard it. As a Roma, Dinicu's post graduation options in the classical music world dwindled. He was accepted for post-graduate studies at the Vienna Conservatory, only to see his admission rescinded because of his Romany background. At the time, Dinicu was already a virtuoso violonist, coming from a long tradition of musicians. His own interpretation does exist on Youtube, and while Heifetz shows a cool virtuoso version, Dinicu's version leverages the minor mode characteristic of traditional Romanian music with repeated glissandi that stop almost like a screetch to accent it's connection with traditional balades. To a Romanian ear, Dinicu's version aches with emotion. While Heifetz does a quiet position change, Dinicu accents it with a forceful, short, almost screetchy glissando immitating a way of singing common in traditional music. The rest of the differences will likely consist of bowing and fingering differences, but the same music sheet. That famous up/down bow staccatto exists in both versions. Dinicu just does not make that his centerpiece, keeping his focus on highlighting the minor mode instead..
While his career as a serious composer in Enescu's vein dwindled for him, he went on to become a successful composer of "light music", writing hundreds of popular songs that launched many crooner careers. He did write a few other fast paced short pieces (check our Hora Martisor) -- and they all live in the public domain under his name. But Hora Staccatto is now associated with Heifetz' name in the western world.
PS_ it is unclear, from what I read, exactly how his Roma background affected his access to the Vienna Conservatory: Was he prevented from leaving? Was funding from such a trip withheld by the Romanian side (unfortunately Roma have a long history of discrimination within Romania)? Did someone write to the admission committee, drawing their attention to his ethnicity? Did they bluntly ask and turned around? I'm very curious to find out.
Regardless, being a violin virtuoso as a Roma was -- and in certain circles, still is -- diminished by the "it's in their genes" stereotype in Europe. This dismisses the countless hours spent refining the skill that people like Dinicu, Ion Voicu, and so many others spent, as well as the enormous talent and towering musical knowledge. I so wish Dinicu had had a chance to grow into the classical composer that weaves folk music into his work, supported by the intellectuals of his country, the same was Enescu was...
Instead, he gave us a few gems, some of which were made famous by others. You may also want to check out his Ciocirlia (The Lark), where he makes his violin sound just like a songhbird -- something that later on was popularized by George Enescu and, stunningly, by George Zamfir on the panflute.
Here are some fun links:
Dinicu's original version:
https://youtu.be/QFbPLEW2oaM?feature=shared
Hora Martisor, as played by Ion Voice (title attribution is incorrect on this video):
https://youtu.be/dOOdhT5csU8?feature=shared
Ciocirlia, Dinicu/ Enescu, as played by Gabriel Croitoru on Violin and small taraf orchestra
https://youtu.be/IoKA1dvRiIU?feature=shared
Ciocirlia, panflute, Gheorghe Zamfir:
https://youtu.be/QzyoqDz04v4?feature=shared
... there are many other amazing gems composed by Griigoras Dinicu. I am just finding them, thanks to the power of the internet
Back to the original version, I ended up buying a copy of Heifetz' Hora Staccatto for piano and violin. It is not in the public domain, and I'm holding it as a future goal in my Violin journey. I have not seen the original version, and I do not believe it is published anywhere other than finding an old edition in some Bucharest antiquities store...