According to Wikipedia, the game was westernised (rewritten story).
[url=https://en.wikipedia.org/wiki/The_Void_(video_game)#Editions_and_titles]https://en.wikipedia.org/wiki/The_Void_(video_game)#Editions_and_titles[/url]

The Void (English edition) is essentially what you'll get when buying this.

It is, however, possible thanks to the last updates provided and fan efforts to play the Polish version with the Russian version's text(s) and audio - https://www.gog.com/forum/void_the/any_chance_of_russian_version/post24

To check if I understand it correctly:
So the "rewritten story" is basically a different translation but the same gameplay/videos/etc?
And the patch adds english subtitles for the russian audio, trying to be as close as possible?

One of the developers (the writer, if I remember correctly) covered some of the major differences on Ice-Pick Lodge's forum for the game: http://forum.ice-pick.com/viewtopic.php?f=28&t=9043#p94905 That is my understanding of it, though I must admit I have had no cause/desire to go back and play it with the patch (I'm among a small number who aren't displeased by the game's English version, I guess).

What i remeber is that it also includes a less steep difficulty curve. If you're intrested in the original I believe you can find it on torrents and believe me - it throws you right into action. It also doesn't tell you explicitly some crucial things, leaving them to be interpreted.

So...the game itself was changed? Some levels are skipped?

After release of the original Ice pich noticed that it was hard as balls and tweked it. It also looks like they added tutorial sequence so you don't get kicked into action without a clue of what is happening.
Regarding levels - there's no levels in Turgor (I'll be using original russian name as it is same in both releases). You are making your way from one point of global map to another and said map stays the same. The way you move (especially how you open sisters' hearts; it'll make sense in the game) is also the same. Characters you meet are the same. It's just that in the void you are told more explicitly what to do. And maybe the void has more story. It also looks like some minor dialogue got changed and now you can feed the first sister color (before she refused every drop) which means you may be able to open her hearts and make her ascend.